Question

Calc II Question

Find the area of the shaded region

Answer 1

`\displaystyle A=-(10)/(3)+(1-e^2)/(e)\approx-5.864`

Explanation:

`\displaystyle A=\int^1_(-1)(y^2-2-e^y)\,dy\\\\A=(y^3)/(3)-2y-e^y\biggr|^1_(-1)\\\\A=\biggr((1^3)/(3)-2(1)-e^1\biggr)-\biggr(((-1)^3)/(3)-2(-1)-e^(-1)\biggr)\\\\A=\biggr((1)/(3)-2-e\biggr)-\biggr(-(1)/(3)+2-(1)/(e)\biggr)\\\\A=(2)/(3)-4-e+(1)/(e)\\\\A=-(10)/(3)+(1-e^2)/(e)\\\\A\approx-5.864`