Integration Quiz

 $\int\ \frac{x}{\sqrt{4-x^2}}dx$  

•  $2\sqrt{4-x^2}+C$  

•  $\sin^{-1}\left(\frac{x}{2}\right)\ +C$  

•  $-\sqrt{4-x^{2\ }}+C$  

•  $-\frac{1}{2}\ln\ \sqrt{4-x^2}+C$  

If  $\int_2^{-8}\ g\left(x\right)dx\ =\ -4\$  and  $\int_2^5\ g\left(x\right)dx\ =\ 6$  , what is  $\int_{-8}^5g\left(x\right)\ dx?$  

• 10

• 2

• -2

• -10

 $\int\ \frac{\left(2+\ln x\right)^{3\ }}{x}dx$  

•  $\left(2+\ln x\right)^{4\ }+C$  

•  $\frac{1}{4}\left(2+\ln x\right)^{4\ }+C$  

•  $\left(2+\ln x\right)^3+C$  

•  $\frac{1}{2}\left(2+\ln x\right)^{2\ }+C$  

The table below shows the rate of water flow w(t)  through a pipe, in gallons per hour from  $0\le t\le12$    hours. Estimate the total amount of water that flowed through the pipe, in gallons, for the 12-hour period by using a mid-point Riemann Sum with three sub-intervals.

• 360 Gallons

• 118 Gallons

• 166 Gallons

• 180 Gallons

A particle is moving along the x-axis with a velocity of   $v\left(t\right)\ =\ 8\cos\left(\frac{t}{2}\right)$  

The particle is at  $x=2$  when  $t=0$ . Find the position of the particle when  $t\ =\ \pi$  .

• 18

• -14

• -16

• 10