Integration .Area enclosed between curves???
Hey I thought when you integrate you find area under the curve :/
I understand how to tackle this question.I found the correct area above the x-axis (1/12) but I don't understand why you integrate with respect to x to find the area below the x-axis -the one above the exponential curve .shouldn't you rearrange the equation and express it in terms of x and then integrate with respect to y.But then again it's C3 u can't integrate the natural logarithm till C4
It's Q5 on the mark scheme btw
I really don't understand -.-
MS
Posted from TSR Mobile
I understand how to tackle this question.I found the correct area above the x-axis (1/12) but I don't understand why you integrate with respect to x to find the area below the x-axis -the one above the exponential curve .shouldn't you rearrange the equation and express it in terms of x and then integrate with respect to y.But then again it's C3 u can't integrate the natural logarithm till C4
It's Q5 on the mark scheme btw
I really don't understand -.-
MS
Posted from TSR Mobile
Original post by livealittle
Hey I thought when you integrate you find area under the curve :/
I understand how to tackle this question.I found the correct area above the x-axis (1/12) but I don't understand why you integrate with respect to x to find the area below the x-axis -the one above the exponential curve .shouldn't you rearrange the equation and express it in terms of x and then integrate with respect to y.But then again it's C3 u can't integrate the natural logarithm till C4
It's Q5 on the mark scheme btw
I really don't understand -.-
MS
Posted from TSR Mobile
I understand how to tackle this question.I found the correct area above the x-axis (1/12) but I don't understand why you integrate with respect to x to find the area below the x-axis -the one above the exponential curve .shouldn't you rearrange the equation and express it in terms of x and then integrate with respect to y.But then again it's C3 u can't integrate the natural logarithm till C4
It's Q5 on the mark scheme btw
I really don't understand -.-
MS
Posted from TSR Mobile
Just integrate each curve separately w.r.t. x and remember to take the absolute value of the exponential one since it's below the x axis. Then just sum the areas up.
Integrating w.r.t. y would give the sideways area, but it's not required and a lot more effort than integrating normally. You would also have to do quite a bit of rearranging for the limits so there's not really any point.
Original post by livealittle
Hey I thought when you integrate you find area under the curve :/
I understand how to tackle this question.I found the correct area above the x-axis (1/12) but I don't understand why you integrate with respect to x to find the area below the x-axis -the one above the exponential curve .shouldn't you rearrange the equation and express it in terms of x and then integrate with respect to y.But then again it's C3 u can't integrate the natural logarithm till C4
It's Q5 on the mark scheme btw
I really don't understand -.-
MS
Posted from TSR Mobile
I understand how to tackle this question.I found the correct area above the x-axis (1/12) but I don't understand why you integrate with respect to x to find the area below the x-axis -the one above the exponential curve .shouldn't you rearrange the equation and express it in terms of x and then integrate with respect to y.But then again it's C3 u can't integrate the natural logarithm till C4
It's Q5 on the mark scheme btw
I really don't understand -.-
MS
Posted from TSR Mobile
There's no need for any "y-integration" here.
If you integrate the "top function" between x = 0 and x = 1/2 you will get a positive number that represents the area between the top curve and the x-axis.
If you integrate the "bottom function" between x = 0 and x = 1/2 you will get the area between curve and axis but with a negative sign because the curve lies below the axis.
So you just need to take the absolute value of the 2nd number and add it to the first result to get the total area.
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