Applications of the Integrals Test

Result

Applications of the Integrals Test - 7

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Weekly Quiz Competition

Question 1
1 / -0.25

The area lying in the first quadrant and bounded by the curve y = x³ , the x –axis and the ordinates at x = - 2 and x = 1 is

A
6

B
3

C
15/4

D
2

Solution

Required area :
Question 2
1 / -0.25

Area bounded by the curves satisfying the conditions is given by

A
15/2 (π/2 - 1) sq. units

B
15/4 (π/2 - 1) sq. units

C
15 (π/2 - 1) sq. units

D
30 (- 1) sq. units

Solution
Question 3
1 / -0.25

The area of the figure bounded by y = e^x , y = e^−x and the straight line x = 1 is

A
e + 2/e

B
e –1/e

C
e + 1/e - 2

D
none of these

Solution
Question 4
1 / -0.25

The area bounded by the parabolas y = (x+1)² and y = (x −1)² and the line y = (1/4) is equal to

A
4/3

B
1/3

C
1/6

D
4

Solution

Required area :
Question 5
1 / -0.25

The area enclosed between the curve y = log_e (x+e) and x = log_e 1/y and the x- axes is

A
3 sq. units

B
1 sq. units

C
2 sq. unit

D
none of these

Solution

Required area is :
Question 6
1 / -0.25

The area bounded by the curve y = x³ , the x –axis and two ordinates x = 1 and x = 2 is

A
17/2 sq. units

B
15/2 sq. units

C
15/4 sq. units

D
17/4 sq. units

Solution
Question 7
1 / -0.25

The area bounded by the parabola y = x² + 1 and the straight line x + y = 3 is given by

A
45/7

B
9/2

C
25/4

D
none of these

Solution

The two curves parabola and the line meet where,

Required area ;
Question 8
1 / -0.25

The area enclosed between the curves y = √x , x = 2y+3and the x-axis is

A
9

B
18

C
27

D
none of these

Solution

The two curves meet where;

Therefore, the two curves meet where x = 9.
Therefore,required Area:
Question 9
1 / -0.25

The area of the region {(x , y) : x² +y² ⩽1 ⩽x+y} is equal to

A
1/2 sq. units

B
sq.units

C
sq. units

D
none of these

Solution

x² +y² = 1,x+y = 1
Meets when
x² (1 −x)² = 1
⇒x² +1+x² −2x = 1
⇒2x² −2x= 0 ⇒2x(x −1)=0
⇒x = 0,x = 1.
i.e. points (1 ,0) ,(0 ,1). Therefore , required area is ;
Question 10
1 / -0.25

The area bounded by y = |sinx| , the x –axis and the line |x| = πis

A
6 sq. units

B
2 sq. units

C
4 sq. units

D
none of these

Solution

Required area :