find the area of the region

Question

y=e^x, y=x^2-1, x=-1,x=1

I have worked this out and i got e-1/e-4/3 and it says im wrong can someone help and understand what i'm doing wrong. i use the formula integral from -1 to 1 (top - bottom)

Answer 1

Area under y= eˣ, above y = x² - 1, between x = -1, x = 1

A = ∫₋₁¹ (eˣ - (x² - 1)) dx = (eˣ - x³/3 + x) | ₋₁¹ = (e - 1/3 + 1) - (1/e + 1/3 - 1) ==>

A = e - 1/e - 2/3 + 2 ==> A = 4/3 + e - 1/e

Answer 2

To find the area of the region bounded by the curves from x=-1 to x=1, we simply subtract the top function from the bottom function and integrate the result on the given bounds to find the area. Finding that y=e^x is the top function, we obtain ∫e^x-(x^2-1) from x=-1 to x=1. The problem in your answer was the -4/3, as the double negative in the integrand will result in a +4/3