# 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

Over the limits of integration, the parabolic function is greater than the linear function, this is why it is a good idea to sketch the region first so that you can see more clearly what you need to do. Over the limits of integration, the parabolic function is greater than the linear function, this is why it is a good idea to sketch the region first so that you can see more clearly what you need to do. 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 $$\displaystyle |\pi\rangle$$