Single integrals

 $\int_{ }^{ }\sin^3\left(x\right)\sin\left(2x\right)dx$  =

•  $-2\cos\left(2x\right)+C$  

•  $2\sin^2\left(x\right)\cos\left(x\right)+C$  

•  $\frac{\sin^4\left(x\right)}{4}\cos\left(x\right)+C$  

•  $\frac{2}{5}\sin^5\left(x\right)+C$  

 $\int_{-5}^{10}\left|2x-6\right|dx$  =

 $\int_0^{\ln2}\sinh^2\left(x\right)\cosh\left(x\right)dx$  =

•  $-\frac{3}{45}$  

•  $\frac{45}{67}$  

•  $\frac{9}{64}$  

•  $\frac{1}{2}$  

The acceleration of a moving object is given by

 $a\left(t\right)=v'\left(t\right)=\left(2t-1\right)\cdot\left(4t^2-4t+1\right)$  and the velocity at time t = 0 is  $v\left(0\right)=2$  m/s. Find  $v\left(t\right)$ . 

•  $\frac{1}{8}\left(4t^2-4t+1\right)^2+\frac{15}{8}$  

•  $-t^4+2t+\frac{1}{8}-14$  

•  $2t^4-4t^3+3t^2-t$  

•  $\frac{4t^2-4t+16}{8}$