AP Calc AB Review for QZ 32-33

$\int\frac{1}{x}dx=$

• $\ln\left|x\right|+C$

• $-\frac{1}{x^2}+C$

• $\frac{1}{x^2}+C$

• 1

Tags

integration and transcendentals

$\int_{ }^{ }xe^{-3x^2}dx=$

• $-\frac{1}{6}e^{-3x^2}+C$

• $\frac{1}{3}e^{-3x^2}+C$

• $-\frac{1}{3}e^{-3x^2}+C$

• $\frac{1}{6}e^{-3x^2}+C$

Tags

integration of transcendentals

$\int_{ }^{ }\frac{4x}{2x^2+6}\ dx=$

• $\ln\left|2x^2+6\right|+C$

• $\ln\left(2x^2+6\right)\left(4x\right)+C$

• $\frac{1}{2x^2+6}+C$

• $\frac{1}{\left(2x^2+6\right)^2}+C$

Tags

integration and transcendentals

A particle moves along an axis so that at any time $t>0$ , its velocity is given by $v\left(t\right)=4-6t^2$ . If the particle is at position $p=7$ when $t=1$ , what is the position of the particle at $t=2$ ?

• -10

• -5

• -3

• 3

Tags

integration and motion

$\int_{ }^{ }\frac{2x}{x^2+1}\ dx=$

• $\ln\left(x^2+1\right)+C$

• $\ln\left|2x\right|+C$

• $\frac{1}{\left(x^2+1\right)^2}+C$

• $\frac{1}{2x}+C$

Tags

integration and transcendentals

$\int_{ }^{ }\frac{e^{\sqrt{x}}}{\sqrt{x}}\ dx=$

• $2e^{\sqrt{x}}+C$

• $\frac{1}{2}e^{\sqrt{x}}+C$

• $2\sqrt{x}e^{\sqrt{x}}+C$

• $e^{\sqrt{x}}+C$

Tags

integration of transcendentals

 $\int_{ }^{ }\cot\left(ab\right)\ db=$  

•  $-\frac{1}{a}\csc^2\left(ab\right)+C$  

•  $\frac{1}{a}\ln\left|\sin\left(ab\right)\right|+C$  

•  $\frac{1}{b}\ln\left|\cos\left(ab\right)\right|+C$  

•  $\frac{1}{b}\ln\left|\sin\left(ab\right)\right|+C$  

Tags

integration and transcendentals

Suppose the velocity function  $v\left(t\right)=6t^2+4t$ and the position function  $s\left(1\right)=2$ . Find $s\left(2\right)$ .

• 4

• 2

• -4

• 22

Tags

integration and motion

A particle moves along the x-axis with a velocity given by $v\left(t\right)=t-t^{\frac{1}{3}}$ for $0\le t\le8$ . If the particle is 4 units to the left of the origin at $t=0$ , where is the particle at $t=8$ ?

• 24 units to the right of the origin

• 20 units to the right of the origin

• 16 units to the right of the origin

• $1\frac{1}{4}$ units to the left of the origin

• $3\frac{1}{12}$ units to the left of the origin

Tags

integration and motion

$\int_0^1\ \frac{e^x}{e^x+1}\ dx=$

• $\ln\frac{e+1}{2}$

• $\ln\left(e+1\right)$

• $\ln\left(2e+2\right)$

• $\ln2$

Tags

integration of transcendentals