AP Calculus AB - Chapter 4 Review -Elearning

Integrate $\int\ \frac{1}{^3\sqrt{x}}\ dx$  

•  $\frac{2x^{\frac{3}{2}}}{3}+c$  

•  $\frac{3x^{\frac{2}{3}}}{2}+c$  

•  $\frac{3x^{\frac{2}{3}}}{2}$  

•  $6x^{\frac{3}{2}}+c$  

Tags

CCSS.7.EE.A.1

Integrate  $\int\frac{2x-1}{\sqrt{x}}\ \ dx$  

•  $\frac{4x^{\frac{3}{2}}}{3}-2x^{\frac{1}{2}}+c$  

•  $\frac{4\sqrt{x}}{3}-2\sqrt{x}+c$  

•  $\frac{4x^{\frac{2}{3}}}{3}-2x^{\frac{1}{2}}+c$  

•  $\frac{4\sqrt{x^3}}{3}-2\sqrt{x}+c$  

Integrate  $\int_{ }\ \frac{x^2+3x-2}{x}\ \ dx$  

•  $\frac{x^2}{2}+3x-2\ln\left|x\right|+c$  

•  $\frac{x^2}{2}+x+c$  

•  $\frac{x^2}{2}+3x+c$  

•  $2x+3$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.B.3

If  $\int_1^3\ f\left(x\right)\ dx\ =5,\ \int_1^{11}\ f\left(x\right)\ dx=24$  and  $\int_1^3\ g\left(x\right)\ dx=7,$  evaluate  $\int_3^{11}\ f\left(x\right)\ dx$  

•  $-19$  

•  $41$  

•  $-11$  

•  $19$  

 $\int_{ }^{ }\left(\cos x+3x^2\right)dx$  

• -sin x + x³ + c

• sinx + x³ + c

• -sin x + 6x + c

• $-\sin x+\frac{x^3}{3}+C$

Estimate the area bounded by f(x) and the x-axis on [-5,5] using the a right rectangle approximation with 4 subintervals.

• 81

• 77.5

• 78

• 75

Estimate the area bounded by f(x) and the x-axis on [-5,5] using the trapezoidal method with 4 trapezoids.

• 159

• 152.5

• 79.5

• 76.25

Tags

CCSS.HSA.SSE.A.1

Determine the exact area of the region bound by the graph of  $y=4x-x^2$  above the x-axis .  

• 63

• 20.833

• 10.667 

• 30

• 39.33

The value of the definite integral for the shaded region on the function  $y=x^3-3x^2+2x$  is: 

• 1.4

• 0.5

• 0.56

• 0

• 0.33

Determine the exact area of the region bound by the graph of  $y=1+\sin x$  above the x-axis on  $\left[0,\frac{3\pi}{2}\right]$  .

•  $\frac{3\pi}{2}$  

•  $\frac{3\pi+2}{2}$  

• 0

•  $\pi$