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Monday, November 16, 2009
Area using Integration
Explain how you would find the area under a curve by using integration.
when finding the area under a curve by using integration we use the equation of the curve for example 2x^2 and integrate within the limit.For example , a is the lower boundary and b is the upper boundary.
integration is the opposite of differentiation take the equation of the curve put it in brackets and substitute x for a and b e a=4 b=2 the equation of the line is 16x^-2 (-16/x)4and 2 (-4)-(-8)= 4units
to find the area under a curve you integrate the equation of the curve -to do this you find the integral of the over all equation -the you substitue the upper and lower boundary into the above and find the difference.
a and b are constants or varibles constants where they represent one number that is shown and varibles are where the number is dependant on other varibles
to find the area under a graph using integration is like taking the graph and cutting and having an upper limit which is "a" and a lower limit which is "b". integration is to find the area between these two point but it is not an exact value of the area only an approximation.
since we are cutting the graph with the limits of "a" and "b". we therefor will have the normal curve bounded by 2 straight lines. but within that curve if we cut it( when i say cut i really mean draw a line from the x-axis to the curve ) and there for we will have more lines which would be limits. the more limits you have is the more precise your area under he graph will be. Since with the more limits u have you will be changing the shape of the graph. into tiny rectangles which are stacked right up next to each other. in which case the area of rectangles are know as l*b and could be found since each interval would be uniform and therefor only one area could be found and multiplied by the number of rectangles.
integration is finding the area under a curve because it finds the area between the two limit and the x axis. the area is found from the x axis to the curve.
integration is use since there is one side that is not a straight line and the area cannot be found using a formula although integration is a formula but there is three straight sides but a curve so area is found for that section only.
f(x) is the equation and a and b are the limits which are the upper limit and lower limit. the upper limit is the larger value and the lower value is the lower limit. f(x) is the equation to which u integrate and use the limits to find the area between the limits.
simple way is to use the "rectangle rule." "divide up" the curve. Then, using these points as the midpoints for the tops of rectangles, you can just redraw this curve in a rising and falling series of rectangles, which looks like a simple bar graph. the approx. areas of each rectangle is then added up
the area under a curve can be found by integrating the equation of the curve, between the values on the x axis you are trying to find the area for. these values on the x-axis are the limits of the integral of the equation, the lower value, a, is subtracted from the higher value, b, for the integral, to give you the area between that range of values.
f(x) is the function and a and b are the variables using the equation of the curve put substitute x for a and b e a=4 b=2 the equation of the line is 16x^-2 (-16/x)4and 2 (-4)-(-8)= 4units
to find the area under a curve first you find the integral of the over all equation then you substitue the upper and lower limits or boundaries and then calculate the difference.
I would first divide the area under the curve into simple shapes if it is irregular. then i would integrate the curve using the limits wrt the shape. i would repeat this for every shape and then find the sum
the area under a curve can be found by integrating the equation of the curve, between the values on the x axis you are trying to find the area for. these values on the x-axis are the limits of the integral of the equation, the lower value, a, is subtracted from the higher value, b, for the integral, to give you the area between that range of values.
he area under a curve can be found by integrating the equation of the curve, between the values on the x axis you are trying to find the area for. these values on the x-axis are the limits of the integral of the equation, the lower value, a, is subtracted from the higher value, b, for the integral, to give you the area between that range of values.
the area under a curve first you find the integral of the over all equation then you sub the upper and lower limits or boundaries then calculate the difference.
f(x) f is the name of the function x is the input value f(x) is the output value....... f(x) is another way of sayin y. it means the output for the given input x.
To find the exact value of the area under a curve y = f(x) from x = a to x = b then you would have to the following: **STEPS** 1)integrate the given function (do not include the K) 2)substitute the upper limit (b) into the integral 3)substitute the lower limit (a) into the integral 4)subtract the second value from the first value
integration can be used to find the area under a graph because a and b are the upper and lower limits or boundaries which enclose the area under the graph.
to find area bounded by the x-axis,the lines x=a and x=b and the curve y=(fx) if y= 3x^2 from this area function we can find the value of y by integrating.
integrating this will give a value of A hence using x=a gives Aa = a^3+k and using x=b gives Ab = b^3+k then using the area between x=a and x=b is given by Ab-Aa where Ab-Aa=(b^3+k)-(a^3+k)=b^3-a^3
now Ab-Aa is referred to as the definite integral from a to b of 3x^2. in this equation a and b are called the boundary values or limits of integration; b is the upper limit and a is the lower limit.
to find the area under a curve you integrate the equation of the curve -to do this you find the integral of the over all equation -the you substitue the upper and lower boundary into the above and find the difference. I am a little confused with where to put the integral sign please dont think i am stupid
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when finding the area under a curve by using integration we use the equation of the curve for example 2x^2 and integrate within the limit.For example , a is the lower boundary and b is the upper boundary.
ReplyDeleteThe area under a curve could be found using integration by using the sum of the rectangles method.
ReplyDeletey=f(x)
F(x) is f is a function of x.
a & b are variables in the equation.
integration is the opposite of differentiation
ReplyDeletetake the equation of the curve put it in brackets and substitute x for a and b e
a=4 b=2 the equation of the line is 16x^-2
(-16/x)4and 2
(-4)-(-8)= 4units
to find the area under a curve you integrate the equation of the curve
ReplyDelete-to do this you find the integral of the over all equation
-the you substitue the upper and lower boundary into the above and find the difference.
f(x)
ReplyDeletethe function of x
or
a function where the varible is x
f(x)=2x-3
a function is where there is a one to one relationship to the other grouping y
a and b are constants or varibles
ReplyDeleteconstants where they represent one number that is shown
and varibles are where the number is dependant on other varibles
hi
ReplyDeleteyou find the area under the curve by integrating the equation of the curve by using the lower and upper boundary.
ReplyDeletea is the upper boundary
b is the lower boundary
f(x) is the equatio of the line
to find the area under a graph using integration is like taking the graph and cutting and having an upper limit which is "a" and a lower limit which is "b". integration is to find the area between these two point but it is not an exact value of the area only an approximation.
ReplyDeletesince we are cutting the graph with the limits of "a" and "b". we therefor will have the normal curve bounded by 2 straight lines. but within that curve if we cut it( when i say cut i really mean draw a line from the x-axis to the curve ) and there for we will have more lines which would be limits. the more limits you have is the more precise your area under he graph will be. Since with the more limits u have you will be changing the shape of the graph. into tiny rectangles which are stacked right up next to each other. in which case the area of rectangles are know as l*b and could be found since each interval would be uniform and therefor only one area could be found and multiplied by the number of rectangles.
ReplyDeletef(x) is a function it is an equation. it is the exact way of writing an equation with out the y. like f(x)=2x+2.
ReplyDeleteGreen Lantern, do you mean that y then is the function of x?
ReplyDeletef(x) simply means that 'f' is a function with respect to 'x'.
ReplyDeleteI'm not sure denith, but i think what green lantern really means is that f(x) can be used in place of 'y' in an equation.
ReplyDeleteintegration is finding the area under a curve because it finds the area between the two limit and the x axis. the area is found from the x axis to the curve.
ReplyDeleteintegration is use since there is one side that is not a straight line and the area cannot be found using a formula although integration is a formula but there is three straight sides but a curve so area is found for that section only.
ReplyDeletef(x) is the equation and a and b are the limits which are the upper limit and lower limit. the upper limit is the larger value and the lower value is the lower limit. f(x) is the equation to which u integrate and use the limits to find the area between the limits.
ReplyDeleteFinding the area under a graph using integration you can use the rectangle rule.
ReplyDeletesimple way is to use the "rectangle rule." "divide up" the curve. Then, using these points as the midpoints for the tops of rectangles, you can just redraw this curve in a rising and falling series of rectangles, which looks like a simple bar graph. the approx. areas of each rectangle is then added up
ReplyDeleteTo find the area under a curve using integration we can use the rectangle method or rule(the sum of areas of the rectangles)
ReplyDeletea and b are variables
ReplyDeletef(x)is a function
f(x) means
ReplyDeletethe function of x or a function where the varible is x.A function can be a one to one relationship or many to one
the area under a curve can be found by integrating the equation of the curve, between the values on the x axis you are trying to find the area for. these values on the x-axis are the limits of the integral of the equation, the lower value, a, is subtracted from the higher value, b, for the integral, to give you the area between that range of values.
ReplyDeletef(x) is the equation of the curve
ReplyDeletea is the lower limit of the integral
b is the higher limit of the integral
Integration is the opposite of Differentiation
ReplyDeletef(x) is the function and a and b are the variables using the equation of the curve put substitute x for a and b e
ReplyDeletea=4 b=2 the equation of the line is 16x^-2
(-16/x)4and 2
(-4)-(-8)= 4units
to find the area under a curve
ReplyDeletefirst you find the integral of the over all equation then you substitue the upper and lower limits or boundaries and then calculate the difference.
f(x)
ReplyDeletef is the name of the function
x is the input value
f(x) is the output value
a and b are the upper and lower limits or boundaries which enclose the area under the graph
ReplyDeletehttp://i50.tinypic.com/2ni0glt.png
I would first divide the area under the curve into simple shapes if it is irregular.
ReplyDeletethen i would integrate the curve using the limits wrt the shape.
i would repeat this for every shape and then find the sum
f(x) is another way of sayin y. it means the output for the given input x.
ReplyDeletea and b are the variables representing the upper and lower limits in calculating the area under the graph
ReplyDeletef(x) is a function where the varible is x
ReplyDeletef(x)=4x+2 is an example
a and b are constants
ReplyDeleteand this represents the lower boundry= a
the upper boundry= b
y=f(x)
ReplyDeleteF(x) is f is a function of x.
a & b are variables in the equation.
you find the area under the curve by integrating the equation of the curve by using the lower and upper boundary.
ReplyDeletea is the upper boundary
b is the lower boundary
f(x) is the function
the area under a curve can be found by integrating the equation of the curve, between the values on the x axis you are trying to find the area for. these values on the x-axis are the limits of the integral of the equation, the lower value, a, is subtracted from the higher value, b, for the integral, to give you the area between that range of values.
ReplyDeletef(x) is the equation of the curve
ReplyDeletea is the lower limit of the integral
b is the higher limit of the integral
y=f(x)
ReplyDeleteF(x) is f is a function of x.
a & b are the bounds 4 the integral
you find the area under the curve by integrating the equation of the curve between the lower and upper bounds.
ReplyDeletea is the upper bound
b is the lower bound
f(x) is the function
he area under a curve can be found by integrating the equation of the curve, between the values on the x axis you are trying to find the area for. these values on the x-axis are the limits of the integral of the equation, the lower value, a, is subtracted from the higher value, b, for the integral, to give you the area between that range of values.
ReplyDeletethe area under a curve
ReplyDeletefirst you find the integral of the over all equation
then you sub the upper and lower limits or boundaries
then calculate the difference.
f(x)
ReplyDeletef is the name of the function
x is the input value
f(x) is the output value.......
f(x) is another way of sayin y. it means the output for the given input x.
To find the exact value of the area under a curve y = f(x) from x = a to x = b then you would have to the following:
ReplyDelete**STEPS**
1)integrate the given function (do not include the K)
2)substitute the upper limit (b) into the integral
3)substitute the lower limit (a) into the integral
4)subtract the second value from the first value
The answer will be a number
integration can be used to find the area under a graph because a and b are the upper and lower limits or boundaries which enclose the area under the graph.
ReplyDeleteto find area bounded by the x-axis,the lines x=a and x=b and the curve y=(fx)
ReplyDeleteif y= 3x^2
from this area function we can find the value of y by integrating.
integrating this will give a value of A
ReplyDeletehence using x=a gives Aa = a^3+k
and using x=b gives Ab = b^3+k
then using the area between x=a and x=b is given by Ab-Aa where Ab-Aa=(b^3+k)-(a^3+k)=b^3-a^3
now Ab-Aa is referred to as the definite integral from a to b of 3x^2.
ReplyDeletein this equation a and b are called the boundary values or limits of integration; b is the upper limit and a is the lower limit.
whenever a definite integral is calculated, the constant of the integration disappears.
ReplyDeleteintegrate the curve and then sub the upper limit into the integral and sub the lower limit also. subtract the lower limit from the upper limit.
ReplyDeletethe area u want to find is bounded by three lines the curve, and two boundaries from the x axis
ReplyDeletethus trapping the area .
ReplyDeleteto find the area under a curve you integrate the equation of the curve
ReplyDelete-to do this you find the integral of the over all equation
-the you substitue the upper and lower boundary into the above and find the difference.
I am a little confused with where to put the integral sign please dont think i am stupid