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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

I got stuck on an old exam

determine the area of the finite region bounded by the curves \(\displaystyle y^2=1-x\) and \(\displaystyle y=x+1\) the integration becomes more easy if we change it to x so lets do it

\(\displaystyle x=1-y^2\) and \(\displaystyle x=y-1\)

to calculate the limits we equal them

\(\displaystyle y-1=1-y^2 <=> x_1=-2 \ x_2=1\)

so we take the right function minus left so we got

\(\displaystyle \int_{-2}^1 y-1-(1-y^2) <=> \int_{-2}^1 y+y^2-2\) and I get the result \(\displaystyle - \frac{9}{2}\) and that is obviously wrong... What I am doing wrong?

Regards,

\(\displaystyle |\pi\rangle\)