AP Calculus Integrals Review

 $\int_1^8\left(x^{\frac{1}{3}}+1\right)dx$  

• 1

• 73/4

• -87/4

• 13/4

 $f\left(x\right)=\frac{1}{\sqrt{x}}$  Find the average value of the function over [4, 9]

• 2

• 1

• 2/5

• 1/5

Find F'(x) given  $F\left(x\right)=\int_0^{x^2}\csc^2x\ dx$  

•  $\csc^2\left(x^2\right)$  

•  $\csc^2\left(x\right)$  

•  $2x\csc^2\left(x\right)$  

•  $2x\csc^2\left(x^2\right)$  

 $\int_{ }^{ }x\left(1-3x^2\right)^4dx$  

•  $\frac{-1}{30}\left(1-3x^2\right)^5$  

•  $\frac{-1}{30}\left(1-3x^2\right)^5+C$  

•  $\left(1-3x^2\right)^5+C$  

•  $\frac{-1}{6}\left(1-3x^2\right)^5+C$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

 $\int_{ }^{ }\left[5^x-\csc^2x\right]dx$  

•  $5^x-\cot x+C$  

•  $5^x+\cot x+C$  

•  $\frac{5^x}{\ln5}+\cot x+C$  

•  $\frac{5^x}{\ln x}-\cot x+C$  

 $2\pi\int_0^1\left(y+1\right)\sqrt{1-y}dy$  

•  $\frac{14}{15}$  

•  $\frac{-28\pi}{15}$  

•  $\frac{-14}{15}$  

•  $\frac{28\pi}{15}$  

Use the trapezoidal rule with n = 4 to estimate (to the nearest thousandth)  $\int_1^2\left(\frac{1}{1+x^3}\right)dx$  

• .257

• .514

• 2.056

• 1.028

A ball is thrown vertically upward from ground level with an initial velocity of 40 m/sec. (note:  $a\left(t\right)=-9.8\ \frac{m}{\sec^2}^{ }$  ).  When will the velocity of the ball be 1/2 of the initial velocity?

• 4.08 sec

• 2.04 sec

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Approximate the area using a Midpoint Riemann Sum on the interval [0,4] for  $f\left(x\right)=x^2+3$  

• 42

• 26

• 33

• 66

Find the number(s) c guaranteed by the MVT for integrals. $\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}}\left(\sec x\tan x\right)dx$  

• 0

• there is no c on [0,4] that satisfies the MVT for integrals

•  $\frac{\pi}{4}$  

•  $\frac{-\pi}{4}$