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Area finite region bounded by the curves

Petrus

Well-known member
Feb 21, 2013
739
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

Administrator
Staff member
Feb 24, 2012
13,775
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. :D
 

Petrus

Well-known member
Feb 21, 2013
739
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. :D
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 :)

Regards,
\(\displaystyle |\pi\rangle\)