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C3/C4 Area under curve/Integration help

Hi guys
Im doing q8 iv in the paper below. I generally get these questions wrong. The style is 'find the area under the curve f(x) between 2 points'. Then the following question says find the area under the curve g(x) which is a translation of the curve f(x). Is there some general rule for finding the area??

( http://www.mei.org.uk/files/papers/c3_paper_jan13.pdf)

in this example i cant see why i should 1 x pi/4 to the answer

thanks for any help
Original post by starwarsjedi123
Hi guys
Im doing q8 iv in the paper below. I generally get these questions wrong. The style is 'find the area under the curve f(x) between 2 points'. Then the following question says find the area under the curve g(x) which is a translation of the curve f(x). Is there some general rule for finding the area??

( http://www.mei.org.uk/files/papers/c3_paper_jan13.pdf)

in this example i cant see why i should 1 x pi/4 to the answer

thanks for any help


g(x)g(x) is a translation of f(x)f(x) π4\frac{\pi}{4} to the right and 11 up.

So the area under g(x)g(x) between π4\frac{\pi}{4} and π2\frac{\pi}{2} is clearly the same as the area under f(x)f(x) between 0 and π4\frac{\pi}{4}, if g(x)g(x) is just f(x)f(x) shifted to the right.

But g(x)g(x) is also f(x)f(x) shifted 11 up and so this creates a rectangle with dimensions 11
and π4\frac{\pi}{4} underneath it, so you add this on.

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