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C3 : APPLICATIONS OF DEFINITE INTEGRALS (Set 1)

Total questions: 10

Worksheet time: 18mins

Name
Class
Date
1.

Using the areas of each region given
 bdf(x)=\int_b^df\left(x\right)=  

a)

2

b)

22

c)

-2

d)

3

2.

The area of the region bounded by the curve y = x2 and the line y = 16

a)

32/3

b)

256/3

c)

64/3

d)

128/3

3.

Then what is the result of  \int_0^3\left(fx\right)dx  

a)

7

b)

5

c)

3

d)

1

4.

Find the enclosed area by the curve with equation  y=4x2y=4-x^2  ,the X-axis and the lines x = -1 and x = 2 

a)

5

b)

7

c)

9

d)

11

5.

If   53g(x)dx=2 \int_{-5}^3g\left(x\right)dx=-2\    and  515g(x)dx=9\int_{-5}^{15}g\left(x\right)dx=9   

Find the value of  153  g(x)dx\int_{15}^3\ \ g\left(x\right)dx  

a)

7

b)

11

c)

- 11

d)

- 7

6.

What is the solution of  15x2dx\int_1^5\left|x-2\right|dx  

a)

7

b)

5

c)

3

d)

1

7.

Find the enclosed area by the curve with equation y=x29 y=x^2-9\  and the X-axis in the region  [1,2]\left[-1,2\right]   

a)

10

b)

18

c)

20

d)

24

8.

Find the enclose area by the curve with equation f(x) = 2x2 f\left(x\right)\ =\ 2-x^2\   and  g(x)=xg\left(x\right)=-x  

a)

 92\frac{9}{2}  

b)

 102\frac{10}{2}  

c)

 112\frac{11}{2}  

d)

 122\frac{12}{2}  

9.

Find the enclosed area by the curve with equation  f(x)=x24 \ f\left(x\right)=x^2-4\   and  g(x)=82x2g\left(x\right)=8-2x^2  

a)

32

b)

35

c)

36

d)

40

10.

Find the area of the region bounded by the graphs of y = x2 and y = 4x.

a)

32/3

b)

64/3

c)

32

d)

64

e)

32/5