Exam 3 Review -- AB

Integrating by substituting is the equivalent to which derivative technique?

• Power Rule

• Chain Rule

• Quotient Rule

• Product Rule

What's the average value of the function $f\left(x\right)=3x^2-10$  on the interval [0,5]?

• 15

• 75

• 22

• 91

Compute $\int_3^35x-3x^2dx$  

• 45

• 25

• 10

• 0

The expression $5\int_1^4f\left(x\right)dx+5\int_4^7f\left(x\right)dx$ is equivalent to: 

• 0

•  $5\int_4^1f\left(x\right)dx-5\int_7^4f\left(x\right)dx$  

•  $\int_1^75f\left(x\right)dx$  

•  $5\int_{-3}^1f\left(x\right)dx$  

Compute $\int3\cos\left(x\right)dx$  

• 3sin(x)

• 3sin(x)+C

• e^x+C

• -3cos(x)

If $\int_3^7f\left(x\right)dx=5$ , then  $\int_3^7f\left(x\right)+10\ dx=???$   

• 5

• 15

• 45

• 50

Compute $\int x^2\cos\left(x^3\right)dx$  

•  $\frac{x^3}{3}\cos\left(\frac{x^4}{4}\right)+C$  

•  $2x\cos\left(3x^2\right)+C$  

•  $\frac{1}{3}\sin\left(x^3\right)+C$  

•  $\frac{15\pi}{19}$  

Given the integral $\int\frac{\left(\ln\left(x\right)\right)^{10}}{x}dx$ , what's the best choice for u in a u-substitution? 

• u=10

• u=1/x

• u=ln(x)^10

• u=ln(x)