Definite Integrals, Properties, AVT

If  $\int_1^5f\left(x\right)dx=8$ , then  $\int_2^2f\left(x\right)dx=$    

• 8

• -8

• 0

• 4

If  $\int_1^8f\left(x\right)dx=5$  and  $\int_4^8f\left(x\right)dx=9$ , then  $\int_1^4f\left(x\right)dx=$    

• -4

• 4

• 8

• 14

If  $\int_0^2f\left(x\right)dx=-3$  and  $\int_0^5f\left(x\right)dx=7$ , then  $\int_2^5\left[4f\left(x\right)-1\right]dx=$   

• 13

• 15

• 37

• 39

If $g\left(x\right)=2f\left(x\right)-4$ on the interval [-2, 8], then  $\int_{-2}^8\left[f\left(x\right)+g\left(x\right)\right]dx=$   

•  $3\int_{-2}^8f\left(x\right)dx-24$  

•  $3\int_{-2}^8f\left(x\right)dx-40$  

•  $3\int_{-2}^8f\left(x\right)dx-4$  

•  $\int_{-2}^8f\left(x\right)dx-40$  

 $\int_1^e\left(\frac{3x^2+1}{x}\right)dx=$  

•  $\frac{3e^2-1}{2}$  

•  $\frac{3e^2+1}{2}$  

•  $e^3+1$  

•  $3e^2-1$  

An object in rectilinear motion moves along the x-axis with velocity v meters per second. If  $v\left(t\right)=3t^2+t-2$ , what is the average velocity of the object during the interval [0, 6]? 

• 37 m/s

• 38 m/s

• 41 m/s

• 222 m/s

 $\int_1^4\sqrt{x}\left(x-\frac{1}{x}\right)dx=$  

•  $\frac{32}{5}$  

•  $\frac{44}{5}$  

•  $\frac{52}{5}$  

•  $\frac{56}{15}$  

The average value of $f\left(x\right)=\sin x$  on the interval  $\left[-\frac{\pi}{3},\frac{\pi}{2}\right]$  is

•  $-\frac{3}{5\pi}$  

•  $\frac{3}{5\pi}$  

•  $\frac{1}{2}$  

•  $\frac{5\pi}{12}$  

 $\int_{-1}^{\sqrt{3}}\left(\frac{1}{x^2+1}\right)dx=$  

•  $\frac{\pi}{12}$  

•  $\frac{7\pi}{12}$  

•  $-\frac{\pi}{12}$  

•  $\frac{5\pi}{12}$  

 $\int_0^{\ln9}e^xdx=$  

• 9

• 8

• 10