BC Calculus Test January 28, 2021

 $\int_{-8}^5f\left(x\right)dx=$  

 $\int_0^{-4}f\left(x\right)dx=$  

What is an appropriate calculus-based justification for the fact that g has an inflection point at x = c. Choose 1.

• f has an inflection point at x = c

• f has a relative minimum at x = c

• f is positive

The graph of the function g is shown. Let

 $f\left(x\right)=\int_{-3}^xg\left(t\right)dt.\$    What is f(1)?

 $g'\left(1\right)=?$  

 $F'\left(x\right)=?$  

The graph of h(x) is shown. What is

 $\int_{-17}^{-9}h\left(x\right)dx?$  

Find

 $\int_{-3}^5f\left(x\right)dx$   Give an exact answer as a multiple of pi.

The graph of f is shown. Let

 $g\left(x\right)=\int_0^xf\left(t\right)dt$  What is an appropriate calculus-based justification for the fact that g is increasing?

• f is positive
  

• f is increasing
  

• f is concave up
  

 $G\left(x\right)=2x^3-4,\ g\left(x\right)=G'\left(x\right)$  Find $\int_1^2g\left(x\right)dx$