The area bounded by 2 curves

[Guest]

Find the area bounded by the curves f(x) = x^2 + 1 and f(x) = x+1

My working out would be


integral of (x+1)^2 - integral of (x^2+1)^2 for the values where they intersect?

Is this correct?

 

[skeeter]

there is no reason to square each function ... the area between the two curves is given by \(\displaystyle \L A = \int_0^1 (x+1) - (x^2+1) dx\)

 

[Guest]

thank you skeeter!

Yeah you are correct...

 

[galactus]

You may also want to try solving it in terms of y to see if you get the same answer.

\(\displaystyle \L\\\int_{1}^{2}(\sqrt{y-1}-(y-1))dy\)