${\displaystyle \underset{0}{\overset{1}{}}}\sqrt[\phantom{2}]{x-x^2}dx=?$

a$)\frac{}{3}$

b$)2$

c$)\frac{}{8}$

d$)\frac{3}{2}$

e$)\frac{5}{4}$

A solid is obtained by rotating the shaded region about $y-$axis. What is the volume of this solid?

a$)(ln2-\frac{1}{3})$

b$)2(ln3-\frac{1}{2})$

c$)2ln2$

d$)(\frac{1}{2}-ln2)$

e$)\frac{2}{3}$

${\displaystyle \underset{0}{\overset{}{}}}\frac{dx}{e^x+e^{-x}}=?$

a$)\frac{}{2}$

b$)\frac{}{4}$

c$)\frac{3}{2}$

d$)\frac{3}{2}$

e$)2$

What is the area of the region enclosed by the curves $y=\frac{1}{4}{x}^2,y=2x^2,x+y=3,x0?$

a$)\frac{4}{3}$

b$)2$

c$)3$

d$)\frac{5}{4}$

e$)\frac{3}{2}$

${\displaystyle \underset{0}{\overset{}{}}}{e}^{cost}sin2tdt=?$

a$)\frac{e}{3}$

b$)\frac{1}{3}$

c$)\frac{1}{2}$

d$)\frac{4}{e}$

e$)$ e