Applications of the Integrals Test

Result

Applications of the Integrals Test - 8

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Weekly Quiz Competition

Question 1
1 / -0.25

If A is the area between the curve y = sin2x , x –axis and the lines x =

A
2

B
1

C
3

D
none of these

Solution

Required area :
Question 2
1 / -0.25

The area bounded by the curves y² = x and y = x² is

A
1/2 sq. units

B
2/3 sq. units

C
1 sq. units

D
none of these

Solution

The two curves meet in (0 , 0) and (1, 1).The required area lies above the curve y = x² and below x = y² and is equal to ;
Question 3
1 / -0.25

The positive value of the parameter a for which the area of the figure bounded by y = sin ax , y = 0 , x = x/a and x = x/3a is 3 is equal to

A
2

B

C
1/2

D
none of these

Solution

We have :
Question 4
1 / -0.25

The area bounded by the parabolas y = 5x² and y −9 = 2x² is

A
12 √3 sq.units

B
6 √2 sq.units

C
12 √2 sq.units

D
4 √3 sq.units

Solution

Required area :
Question 5
1 / -0.25

The area bounded by the curves y = √x , 2y+3 = x and the x –axis in the first quadrant is

A
9

B
18

C
36

D
none of these

Solution

Required area :
Question 6
1 / -0.25

The area bounded by y = 2cosx , x = 0 to x = 2 πand the axis of x in square units is

A
6

B
4

C
8

D
7

Solution

Required area :

Therefore , total area from x = 0 to x = 2 π is 4 X 2= 8 sq. units.
Question 7
1 / -0.25

The area common to the circle x² +y² = 16a² and the parabola y² = 6ax is

A

B

C

D
none of these

Solution

Required area :
Question 8
1 / -0.25

The area bounded by the parabola y² = 4x and the line x + y = 3 is

A
32/3

B
16/3

C
64/3

D
none of these

Solution

Required area :
Question 9
1 / -0.25

The area enclosed by the parabola y² = 2x and its tangents through the point (-2 , 0) is

A
8/3

B
4

C
3

D
none of these

Solution
Question 10
1 / -0.25

The area bounded by the curve y = x log x and y = 2x −2x² is

A
1/2 sq. units

B
7/12 sq. units

C
3/12 sq. units

D
none of these

Solution

Required area :
Question 11
1 / -0.25

The area of the figure bounded by the curve y = log_e x , the x –axis and the straight line x = e is

A
1

B
5 - e

C
3 + e

D
none of these

Solution

Required area :
Question 12
1 / -0.25

The area of the region bounded by the curves y = |x −1| and y = 3 - |x| is

A
3 sq.units

B
4 sq. units

C
6 sq. units

D
2 sq. units

Solution

Required area :
Question 13
1 / -0.25

The area bounded by the curve y = x² +1and the line x + y = 3 is

A
32/3

B
9/2

C
16/3

D
35/3

Solution

The two curves parabola and the line meet where,

Therefore , the required area is :
Question 14
1 / -0.25

The area bounded by the angle bisectors of the lines x² −y² +2y = 1 and x+y = 3 is

A
6 sq. units

B
2 sq. units

C
3 sq.units

D
4 sq. units

Solution

The angle bisectors of the line given by x² −− y² +2y = 1 are x = 0 , y = 1. Required area = 1/2 .2.2 = 2 sq. units
Question 15
1 / -0.25

The area bounded by the curves y= |x −1| and y = 1 is given by

A
2

B
1

C
1/2

D
none of these.

Solution

The given curves are : (i) y = x –1 , x >1 . (ii) y = - (x –1) , x <1. (iii) y = 1 these three lines enclose a triangle whose area is : 1/2 .base.height = 1/2 .2 .1 = 1 sq. unit.