Free Printable Chapter 3 Integration (3.3)

1.

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

a)

$4$

b)

$3$

c)

$2$

d)

$1$

2.

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

a)

$60\frac{5}{6}$

b)

$\frac{366}{6}$

c)

$60\frac{3}{5}$

d)

$\frac{240}{5}$

3.

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

a)

$\frac{1}{3}$

b)

$1\frac{1}{3}$

c)

$-1\frac{1}{3}$

d)

$-\frac{1}{3}$

4.

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

a)

$4$

b)

$3$

c)

$2$

d)

$1$

5.

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

a)

$2$

b)

$1$

c)

$0$

d)

$-1$

6.

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

a)

$12$

b)

$10.5$

c)

$18$

d)

$20$

7.

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.

a)

$-3\frac{7}{9}$

b)

$-3$

c)

$1\frac{7}{9}$

d)

$3\frac{7}{9}$

8.

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

a)

$7\frac{3}{4}$

b)

$7$

c)

$5\frac{3}{4}$

d)

$3$

9.

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.

a)

$100\pi$

b)

$323\pi$

c)

$1\ 215\pi$

d)

$2\ 250\pi$

10.

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.

a)

$8\pi$

b)

$4\pi$

c)

$64\pi$

d)

$\frac{16}{3}\pi$

Chapter 3 Integration (3.3)

Total questions: 10

Worksheet time: 10mins

Similar Resources on Wayground