Part II: Complete each part in order, use correct and complete notation for proper credit.

$14.(8$ points$)$ Let $R$ be the region enclosed by $y=x^2+2x+1$ and $y=1-x.$

a$.(2$ points$)$ Sketch and shade the region $R$ on the grid by labeling functions of curves.

b$.(3$ points$)$ Set up an integral that describes AREA of the region $R.$ Do not simplify the integrand. Do not solve the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{0}{-3}[1+(x^2+2x+1{)}^2-(1-x{)}^2]dx$

c$.(3$ points$)$ Set up an integral that describes the VOLUME of the solid obtained by rotating the region $R$ about the $x-$axis. Do not simplify the integrand. Do not solve the integral.

Disk $={\displaystyle \underset{a}{\overset{b}{}}}(f(x{)}^2-g(x{)}^2)$

$q,\frac{0}{-3}((x^2+2x+1{)}^2-(1-x{)}^2)dx$

$x^2+2x+1=1-x$

$x=-3,0$

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