Gr 12 Quiz

∫ 6 x (x² +1 )² dx

• ( x² + 1)³ + C
• 3 ( x² + 1)³ + C
• ( x² + 1)¹ + C
• 6 ( x² + 1)³ + C

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.B.3

∫ 2x cos(x²) dx

• sin(x²) + C

• 2 sin ( 2x ) + C

• (1/2) sin(x²) + C

• 4 cos(2x ) + C

∫ 2 x (x²- 3)^(1/2) dx

• (x²- 3)^(3/2)+C
• (3/2)(x²- 3)^(3/2)+C
• (2/3)(x²- 3)^(3/2)+C
• (2/3)(x²- 3)^(-1/2)+C

Tags

CCSS.HSA.APR.A.1

CCSS.HSN.RN.A.2

∫ 2x cos(x²) dx

• sin(2x) + C
• 2 sin ( 2x ) + C 
• (1/2) sin(2x) + C 
• 4 cos(2x ) + C

What is the choice of u for ∫ e^x(1+e^x)^(1/2) dx?

• e^x

• 1+e^x

• (1+e^x)^(1/2)

• (e^x)^(1/2)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

CCSS.HSA.SSE.A.2

 $INTEGRATE\ \int\ \ \frac{8x^2}{\left(x^{3\ \ }+2\right)}\ dx\ \ \ \$  

•  $-\frac{4}{\left(x^{3\ \ }+\ 2\right)^2}\ \ +\ C$  

•  $\frac{4}{3\left(x^3\ +2\right)^2}\ +C$  

•  $\frac{4}{\left(x^3\ \ +\ 2\right)^2}\ \ \ +C$  

•  $-\frac{4}{3\left(x^{3\ }+2\right)^2}\ \ +C$  

Use substitution to evaluate the integral $\int4\sec^24x\ \sqrt{\tan4x}\ dx$

• $2\left(\tan4x\right)^{\frac{3}{2}}+C$

• $\frac{15}{4}\cdot\left(\tan4x\right)^{\frac{4}{3}}+C$

• $\frac{4}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C$

• $\frac{2}{3}\cdot\left(\tan4x\right)^{\frac{3}{2}}+C$

 $\int\frac{\left(\ln^6x\right)}{x}\ dx$  

•  $7\left(\ln x\right)^7+C$  

•  $\frac{\ln^6x}{x^2}+C$  

•  $\frac{1}{7}\left(\ln x\right)^7+C$  

•  $\frac{6}{7}\left(\ln x\right)^7+C$  

 $\int10x^2\left(5x^2-4\right)^3dx$  

•  $\left(5x^2-4\right)^4+C$  

•  $4\left(5x^2-4\right)^4+C$  

•  $\frac{1}{4}\left(5x^2-4\right)^4+C$  

•  $5x^2\left(\frac{5}{3}x^3-4x\right)^4+C$  

Use the indicated substitution to evaluate the integral.

 $\int2x\cos(x^2)\ dx\ ,\ \ \ \ u=x^2$  

•  $\sin\left(x^2\right)+C$  

•  $2\sin\left(x^2\right)+C$  

•  $\frac{1}{2}\sin\left(x^2\right)+C$  

•  $4\cos\left(x^2\right)+C$