Integration

Which of the following is TRUE ?

• $\int_{ }^{ }\sin\ x\ \ dx\ =\ \cos\ x\ +c$

• $\int_{ }^{ }e^x\ \ dx\ =\ \frac{e^{x+1}}{x+1}\ +\ c$

• $\int_{ }^{ }\ \frac{1}{x}\ \ dx\ =\ \ln\ \left|x\ \right|\ +c$

• $\int_{ }^{ }\ x\ \ dx\ =\ 1\ +\ c$

 $\int_{ }^{ }x^3\ -\pi\ dx\ \ =$  

•  $3x^2\ +\ c$  

•  $\frac{x^4}{4}\ +\ c$  

•  $\frac{x^4}{4}\ -\ \pi x$  

•  $\frac{x^4}{4}\ -\ \pi x\ +\ c$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

What is  $\int_{ }^{ }\ \frac{5}{x^6}\ dx$  ?

•  $5x^{-6}\ +\ c$  

•  $5x^{-5}\ +\ c$  

•  $-\frac{5}{4x^4}\ +\ c$  

•  $-\frac{1}{x^5}\ +\ c$  

Tags

CCSS.HSA.APR.D.7

Integrate  $\int_{ }^{ }\cos\ \left(5x\right)\ dx$  with respect to x.

•  $\sin\ \left(5x\right)\ +\ c$  

•  $-\frac{1}{5}\sin\ \left(5x\right)\ +\ c$  

•  $\frac{1}{5}\ \sin\ \left(5x\right)\ +\ c$  

•  $\frac{\cos\ \left(5x\right)}{5}\ +\ c$  

Which is the integral of  $\int_{ }^{ }\ \left(5-3x\right)^3\ dx$  ?

•  $3\left(5-3x\right)^2\ +c$  

•  $\frac{\left(5-3x\right)^4}{4}+\ c$  

•  $\frac{\left(5-3x\right)^4}{12}+\ c$  

•  $-\frac{\left(5-3x\right)^4}{12}+\ c$  

Tags

CCSS.HSA.APR.A.1

Which of the following is NOT one of techniques of Integration?

• Substitution

• By Part

• Quotient Rule

• Partial Fraction

Using integration by part, if given that u = (x + 1) then find v for $\int\left(x\ +1\right)\ e^{2x}\ dx$  

•  $\frac{x^2}{2}+x$  

•  $e^{2x}$  

•  $2e^{2x}$  

•  $\frac{e^{2x}}{2}$  

Integrate the partial fraction with respect to x
 $\int_{ }^{ }\ \frac{1}{\left(x\right)}\ +\ \frac{4}{\left(2x\ -1\ \right)}\ dx$  

•  $\ln\ \left|x\right|\ +\ 8\ \ln\left|2x-1\right|+c$  

•  $\ln\ \left|x\right|\ +\ 4\ \ln\ \left|x-1\right|+c$  

•  $\ln\ \left|x\right|\ +\ 4\ \ln\left|2x-1\right|+c$  

•  $\ln\ \left|x\right|\ +\ 2\ \ln\left|2x-1\right|+c$  

Tags

CCSS.HSA.APR.D.6

Evaluate  $\int_1^2\ \ 3x^2\ \ dx$  

•  $7$  

•  $8$  

•  $12$  

•  $x^3$  

Evaluate the integral  $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$  

•  $2$  

•  $4$  

•  $6$  

•  $8$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7