AP Calculus Unit 6A Multiple Choice Qs

 $\int_0^{\frac{\pi}{4}\ }\sin x\ dx\ =$  

•  $-\frac{\sqrt{2}}{2}$  

•  $\frac{\sqrt{2}}{2}$  

•  $-\frac{\sqrt{2}}{2}-1$  

•  $-\frac{\sqrt{2}}{2}+1$  

•  $\frac{\sqrt{2}}{2}-1$  

(No calculators!)

• A

• B

• C

• D

• E

 $\int_1^e\ \frac{x^2-1}{x}dx\ =$  

•  $e-\frac{1}{e}$  

•  $e^2-e$  

•  $\frac{e^2}{2}-e+\frac{1}{2}$  

•  $e^2-2$  

•  $\frac{e^2}{2}-\frac{3}{2}$  

• A

• B

• C

• D

• E

If $\int_{-5}^2\ f\left(x\right)dx\ =\ -17$ and  $\int_5^2\ f\left(x\right)dx\ =-4$  , what is the value of  $\int_{-5}^5\ f\left(x\right)dx$  ?

• -21

• -13

• 0

• 13

• 21

The table gives values of a function  $f$   and its derivative at selected values of x. If  $f'$   is continuous on the interval [-4, -1], what is the value of  $\int_{-4}^{-1}f'\left(x\right)dx$  ?

• -4.5

• -2.25

• 0

• 2.25

• 4.5

If a trapezoidal sum overapproximates  $\int_0^4f\left(x\right)dx$  , and a right Riemann sum underapproximates   $\int_0^4f\left(x\right)dx$   , which of the following could be the graph of  $y=f\left(x\right)$   ?

• A

• B

• C

• D

• E

Tags

CCSS.HSS.IC.B.4

The regions A, B, and C in the figure are bounded by the graph of the function f and the x-axis. If the area of each region is 2, what is the value of  $\int_{-3}^3\left(f\left(x\right)+1\right)dx$  ?

• -2

• -1

• 4

• 7

• 12

• 0

• 1

• 2

• 3

• 4

Tags

CCSS.8.EE.C.7B