Chapter 3 Integration (3.3)

Calculate the value of  $\int_0^13x^2\ dx$ . 

•  $4$  

•  $3$  

•  $2$  

•  $1$  

Find the value of  $\int_{-2}^3\left(5x^2-3x+2\right)\ dx$ . 

•  $60\frac{5}{6}$  

•  $\frac{366}{6}$  

•  $60\frac{3}{5}$  

•  $\frac{240}{5}$  

Find the definite integral for  $x^2\left(x-2\right)$ from  $x=0$  to  $x=2$  .

•  $\frac{1}{3}$  

•  $1\frac{1}{3}$  

•  $-1\frac{1}{3}$  

•  $-\frac{1}{3}$  

Given  $\int_0^3h\left(x\right)\ dx=3$ , find the value of  $\int_0^1h\left(x\right)\ dx\ -\int_3^1h\left(x\right)dx$ .

•  $4$  

•  $3$  

•  $2$  

•  $1$  

Given  $\int_0^ak\left(x\right)dx=2$ , find the value of  $a$  when  $\int_0^a\left[k\left(x\right)+3\right]dx=8$ .

•  $2$  

•  $1$  

•  $0$  

•  $-1$  

The diagram shows a part of the curve  $y=\frac{1}{2}x^2+3$ . Find the area of the shaded region.

•  $12$  

•  $10.5$  

•  $18$  

•  $20$  

The diagram shows a shaded region bounded by the curve  $x=\frac{1}{9}y^3-3$ ,  $y=1$  and the y-axis. Find the area of the shaded region.

•  $-3\frac{7}{9}$  

•  $-3$  

•  $1\frac{7}{9}$  

•  $3\frac{7}{9}$  

Based on the diagram, find the area of the shaded region.

• $7\frac{3}{4}$

• $7$

• $5\frac{3}{4}$

• $3$

The diagram shows a shaded region under the curve  $y=5x^2$ . Find the generated volume, in terms of $\pi$ ,  when the shaded region is revolved through  $360^0$   about the x-axis.

•  $100\pi$  

•  $323\pi$  

•  $1\ 215\pi$  

•  $2\ 250\pi$  

The diagram shows a part of the curve  $y=x^2$ . Find the generated volume, in terms of  $\pi$ , when the region bounded by the curve, the y-axis and the line  $y=4$  is rotated through  $360^0$  about the y-axis.

•  $8\pi$  

•  $4\pi$  

•  $64\pi$  

•  $\frac{16}{3}\pi$