# Exercise 8.2(Application of Integrals)

### Chapter 8 Exercise 8.2 ncert math solution class 12

Question 1: Find the area of the circle which is interior to the parabola .

Solution : The required area is represented by the shaded area OBCDO.

Solving the given equation of circle , and parabola ,

Whent then

we obtain the B Point of intersection as and .

Area Area
We draw BM perpendicular to OA.

Therefore, the coordinates of are .

Therefore, Area OBCO = Area OMBCO – Area OMBO

Therefore, the required area OBCDO =

units.

Question 2: Find the area bounded by curves and .

Solution : The area bounded by curves and is represented by the shaded area OACBO.

On solving the equations, and ,

When then

we obtain the point of intersection as and .

It can be observed that the required area is symmetrical about x-axis.

Area Area OCAO

We join , which intersects at , such that is perpendicular to OC.

The coordinates of are

Area OCAO Area OMAO + Area MCAM

Therefore, required area OBCAO =

.

Question 3: Find the area of the region bounded by the curves and .

Solution: The area bounded by the curves:

Then, Area OCBAO = Area ODBAO – Area ODCO

Question 4: Using integration finds the area of the region bounded by the triangle whose vertices are and .

Solution: BL and CM are drawn perpendicular to x-axis.
It can be observed in the given figure that,

Area Area (BLMCB) – Area (AMCA)

Equation of line segment is

Equation of line segment BC is

Equation of line segment AC is

Area (AMCA)

units

Therefore, from equation (1), we have

Area units

Question 5: Using integration find the area of the triangular region whose sides have the equations and

Solution: The equations of sides of the triangle are , and .

Solving and

When then

Point

Again solving and

Point

Again solving and

Point

we obtain the vertices of triangle as , and

It can be observed that,

Area Area (OLCAO)

units

Question 6: Smaller area enclosed by the circle and the line is

(A)

(B)

(C)

(D)

Solution: The correct answer is (B)

The smaller area enclosed by the circle, and the line, , is represented by the shaded area ACBA.

Area Area

units

Thus, the correct answer is (B).

Question 7: Area lying between the curve and is
(A)

(B)

(C)

(D)

Solution: The correct answer is (B)

The area lying between the curve, and , is represented by the shaded area OBAO.

The points of intersection of these curves are and .

We draw AC perpendicular to -axis such that the coordinates of are .

Area Area

Thus, the correct answer is (B).

## Chapter 8: Application of Integrals Class 12

Exercise 8.1 ncert math solution class 12

Exercise 8.2 ncert math solution class 12

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