Introduction to 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

 $\int_{ }^{ }\left(\frac{1}{7-4x}\right)dx$  

•  $\frac{\left(-\ln|7-4x|\right)}{7}+c$  

•  $\frac{\left(\ln|7-4x|\right)}{4}+c$  

•  $\frac{\left(-\ln|7-4x|\right)}{4}+c$  

•  $\frac{\left(\ln|7-4x|\right)}{7}+c$  

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

•  $2$  

•  $4$  

•  $6$  

•  $8$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.APR.D.6

 $\int\left(\frac{\cos x}{1-\cos x}\right)dx$  

•  $-\operatorname{cosec}x+\cot x+c$  
  

•  $-\operatorname{cosec}x-\cot x+c$  

•  $\operatorname{cosec}x-\cot x+c$  
  

•  $\operatorname{cosec}x+\cot x+c$   $N.O.T$  

 $\int\tan^2\left(5x-10\right)\ dx$  by using method of substitution.

•  $\sec\left(5x-10\right)\tan\left(5x-10\right)+c$  

•  $\tan\left(5x-10\right)-x$  

•  $\frac{\tan\left(5x-10\right)}{5}+c$  

•  $\frac{\tan\left(5x-10\right)}{5}-x+c$  

 $\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$  

•  $-x^{-1}-3x^{-2}+C$  

•  $\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$  

•  $-x^{-1}-3x^{-2}$  

•  $-x-3x^2+C$  

Tags

CCSS.HSA.APR.D.7

If y = $ax^n$  , then  $\int_{ }^{ }y\ dx\ =$  

•  $\frac{ax^{n+1}}{n+1}$  

•  $\frac{ax^{n-1}}{n-1}+\ c$  
  

•  $\frac{ax^{n+1}}{n}+\ c$  

•  $\frac{ax^{n+1}}{n+1}+\ c$  

Tags

CCSS.HSA.APR.A.1

• A

• B

• C

• D