Find the area of the region.

Question

y = e^x,  y = x² − 1,  x = −1,  x = 1

Answer 1

Hi Natalie,

The area between two curves y₁= e^x,  y₂ = x² − 1 is equal to the difference of areas under these two curves which is equal to the integral of difference between y₁ and y₂ on the interval [-1,1]

Int(y₁ - y₂₎dx=Int(  e^x. - x^2+1)dx=e^x-x³/3+x |x=-1 to x=1|

So the result would be

e^x-x³/3+x (taken at x=+1) minus e^x-x³/3+x (taken at x=-1)

Hope that'd help

Dr.Boroda