NCERT Class 12 Mathematics Chapter 8 Application of Integrals

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NCERT Class 12 Mathematics Chapter 8 Application of Integrals

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Application of Integrals

Chapter – 8

Exercise 8.1

1. Find the area of the region bounded by the ellipse x²/16 + y²/9 = 1.

Ans: 

It is given that 

Area of ellipse = 4 × ar (OAB)

= 3π

Area of ellipse = 4 × 3π = 12π units

2. Find the area of the region bounded by the ellipse x²/4 + y²/9 = 1.

Ans: 

It is given that 

⇒ x²/4 + y²/9 = 1

Area of ellipse = 4 × ar (OAB) 

Choose the correct answer in the following Exercises 3 and 4

3. Area lying in the first quadrant and bounded by the circlery x² + y² = 4 and the lines x = 0 and x = 2 is

(Α) π

(B) π\2 

(c) π\3

(D) π\4

Ans: 

Correct answer is A.

4. Area of the region bounded by the curve y² = 4x, y – axis and the line y = 3 is

(A) 2 

(B)  4/9 

(C) 9/3 

(D) 9/2 

Ans: 

Correct answer is B.

Miscellaneous Exercise on Chapter 8

1. Find the area under the given curves and given lines:

(i) y = x², x = 1, x = 2 and x – axis.

Ans: 

(ii) y = x⁴  x = 1, x = 5 and x – axis. 

Ans: 

2. Sketch the graph of y = |x + 3| and evaluate

Ans: 

X	– 6	– 5	– 4	– 3	–  2	– 1	0
Y	3	2	1	0	1	2	3

3. Find the area bounded by the curve y = sin x between x = 0 and x = 2π.

Ans:

Area bounded by the curve = Area OABO + Area BCDB

= 1 + 1 + |(- 1 – 1)| 

= 2 +| – 2| 

= 2 + 2 

= 4

Choose the correct answer in the following Exercises from 4 to 5

4. Area bounded by the curve y = x³, the x – axis and the ordinates x = – 2 and x = 1 is

(A) – 9

(B) -15/4

(C) 15/4

(D) 17/4

Ans: 

required area 

Correct answer is D.

5. The area bounded by the curve y = x lxl, x – axis and the ordinates x = – 1 and x = 1 is given by 

(A) 0 

(B) 1/3

(C) 2/3 

(D) 4/3

[Hint: y = x² if x > 0 and y = – x²  if x < 0].

Ans: 

required area 

 Correct answer is C.