Quiz on Integration of class 11

Which one of the following is the integration of

 $\int_{ }^{ }\ \frac{1}{x^2}dx$  ?

•  $\log_{ }\left(x^2\right)+c$  

•  $x+C$  

•  $-\frac{1}{x}+c.$  

•  $\frac{x^3}{3}+c$  

Evaluate the integral

 $\int_{ }^{ }\frac{\text{1}}{\text{x lnx}}dx.$  

•  $x\ \ln\ x+c.$  

•  $\ln\left(\ln\ x\right)+c$  

•  $\left(\ln\ x\right)^2+c.$  

•  $\ln\ x+c.$  

Find the area under a curve of

 $y=x^2\ from\ x=1\ to\ x=3.$  

•  $\frac{36}{3}$  
  

•  $\frac{26}{3}$  

•  $\frac{16}{3}$  

•  $\frac{46}{3}$  

 $Find\ the\ integral\ of\ \int_{-1}^32dx$  

• 2

• 4

• 6

• 8

What does C represents in anti-derivatives?

• A variable

• Constant

• Unknown

• None

 $Evaluate\ \int_{-4}^4\sqrt{16-x^2}dx$  

•  $16\pi$  

•   $8\pi$ 

•  $128\pi$  

•  $0$  

Which integration does not  represents the shaded area?

•  $2\int_0^a\ \left(x^2-3\right)dx.$  

•  $2\int_{-a}^0\left(x^2-3\right)dx.$  

•  $\int_{-a}^a\left(x^2-3\right)dx.$  

•  $\int_{-a}^a\left(3-x^2\right)dx.$  

Which integration best represents the shaded region?

• $\int_0^{\sqrt{2}}\left(y^2+3\right)dy.$

• $\int_3^5xdx.$

• $\int_3^5\sqrt{x-3}dx$

• $\int_0^{\sqrt{2}}\sqrt{x-3}dx$

Evaluate the integral

 $\int_{ }^{ }xe^xdx$  

•  $xe^x+e^x+c$  

•  $xe^x-e^x+c$  

•  $x+e^x+c$  

•  $x-e^x+c$  

Evaluate

 $\int_{ }^{ }\cos^2xdx$  

•  $\frac{\sin2x}{4}+\frac{x}{2}+c$  

•  $\sin^2x+c$  

•  $-\sin^2x+c$  

• None