# Area finite region bounded by the curves

#### Petrus

##### Well-known member
Hello MHB,
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,
$$\displaystyle |\pi\rangle$$

#### MarkFL

Thanks alot! I learned a lesson this time I did do it in my brain and that was not cleaver! Thanks alot for the fast responed! Now I get $$\displaystyle \frac{9}{2}$$ that is correct
$$\displaystyle |\pi\rangle$$