Fundamental Theorem of Calculus (BPS)

  $\$  If F(x) =   $\int_{-3}^x\sin xdx$  then F'(x) =

• cosx

• sin(-3)

• sinx

•  $\sin\pi$  

 $\$  Which of the following is equivalent to 

 $\int_0^{\pi}\sin xdx$  

•  $\int_0^{\pi}\cos xdx$  

•  $\int_{\pi}^{2\pi}\sin xdx$  

•  $\int_{-\pi}^0\sin xdx$  

•  $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sin xdx$  

•  $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\cos xdx$  

Tags

CCSS.HSA.SSE.B.3

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

• -1/2

• 7/24

• 1/2

• 1

• 2ln2

The graph of a piecewise linear function f  for $-1\le x\le4$  is shown. What is the value of  $\int_{-1}^4f\left(x\right)dx?$  

• 1

• 4

• 8

• 2.5

• 5.5

Tags

CCSS.6.SP.B.4

CCSS.HSS.ID.A.1

 $\$  If F(x) =  $\int_0^x\left(\sqrt{t^3+1\ }\right)dt$   what is F'(2)

• -3

• -2

• 2

• 3

• 18

 $\int_0^5e^{-x^2}dx$  Use your calculator to evaluate

• 5

• 0

• .443

• .886

• 1

 $If\ \ \int_{-2}^5f\left(x\right)dx\ =\ -3\ \ \ \ \ \$  What is the value of  $\int_5^{-2}f\left(x\right)dx\ =$  

• -3

• 0

• 3

• 7

 $\$  Find the area between y = -x and  $y=x^2$  on [0,2]

• 2/3

• 8/3

• 4

• 14/3

• 16/3

Tags

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.11

 $If\ \int_2^6f\left(x\right)dx=10$ then  $\int_2^6\left(f\left(x\right)+5\right)dx=$  

• 15

• 50

• 30

• 20

• 10

 $\int_{\pi}^{2\pi}\theta d\theta=$  

•  $\pi^2$  

•  $\frac{3\pi^2}{2}$  

•  $3\pi^2$  

•  $6\pi^2$