# NCERT Solutions for Class 12 Maths Maths Part-2 Chapter 8

## Application of Integrals Class 12

### Exercise 8.1 : Solutions of Questions on Page Number : 365

Q1 :

Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.

Answer : The area of the region bounded by the curve, y2 = x, the lines,x = 1 and x = 4, and the x-axis is the area ABCD. Answer needs Correction? Click Here

Q2 :

Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

Answer : The area of the region bounded by the curve, y2 = 9x, x = 2, and x = 4, and the x-axis is the area ABCD. Answer needs Correction? Click Here

Q3 :

Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

Answer :

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Q4 :

Find the area of the region bounded by the ellipse Answer :

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Q5 :

Find the area of the region bounded by the ellipse Answer :

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Q6 :

Find the area of the region in the first quadrant enclosed by x-axis, line and the circle Answer :

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Q7 :

Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line Answer :

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Q8 :

The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.

Answer :

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Q9 :

Find the area of the region bounded by the parabola y = x2 and Answer :

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Q10 :

Find the area bounded by the curve x2 = 4y and the line x = 4y - 2

Answer :

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Q11 :

Find the area of the region bounded by the curve y2 = 4x and the line x = 3

Answer :

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Q12 :

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

A. π

B. C. D. Answer :

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Q13 :

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

A. 2

B. C. D. Answer :

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### Exercise 8.2 : Solutions of Questions on Page Number : 371

Q1 :

Find the area of the circle 4x2 + 4y2 = 9 which is interior to the parabola x2 = 4y

Answer :

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Q2 :

Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 3

Answer :

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Q3 :

Using integration finds the area of the region bounded by the triangle whose vertices are (-1, 0), (1, 3) and (3, 2).

Answer :

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Q4 :

Using integration find the area of the triangular region whose sides have the equations y = 2x +1, y = 3x + 1 and x = 4.

Answer :

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Q5 :

Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is

A. 2 (π - 2)

B. π - 2

C. 2π - 1

D. 2 (π + 2)

Answer :

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Q6 :

Area lying between the curve y2 = 4x and y = 2x is

A. B. C. D. Answer :

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### Exercise Miscellaneous : Solutions of Questions on Page Number : 375

Q1 :

Find the area under the given curves and given lines:

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

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

Answer :

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Q2 :

Find the area between the curves y = x and y = x2

Answer :

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Q3 :

Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 1 and y = 4

Answer :

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Q4 :

Sketch the graph of and evaluate Answer :

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Q5 :

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

Answer :

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Q6 :

Find the area enclosed between the parabola y2 = 4ax and the line y = mx

Answer :

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Q7 :

Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12

Answer :

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Q8 :

Find the area of the smaller region bounded by the ellipse and the line Answer :

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Q9 :

Find the area of the smaller region bounded by the ellipse and the line Answer :

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Q10 :

Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis

Answer :

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Q11 :

Using the method of integration find the area bounded by the curve [Hint: the required region is bounded by lines x + y = 1, x â€“ y = 1, â€“ x + y = 1 and â€“ x â€“ y = 11]

Answer :

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Q12 :

Find the area bounded by curves Answer :

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Q13 :

Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x - 2y = 6 and x - 3y + 5 = 0

Answer :

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Q14 :

Find the area of the region Answer :

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Q15 :

Area bounded by the curve y = x3, the x-axis and the ordinates x = â€“2 and x = 1 is

A. â€“ 9

B. C. D. Answer :

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Q16 :

The area bounded by the curve , x-axis and the ordinates x = â€“1 and x = 1 is given by

[Hint: y = x2 if x > 0 and y = â€“x2 if x < 0]

A. 0

B. C. D. Answer :

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Q17 :

The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is

A. B. C. D. Answer :

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Q18 :

The area bounded by the y-axis, y = cos x and y = sin x when A. B. C. D. Answer :

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Maths Part-2 - Maths : CBSE NCERT Exercise Solutions for Class 12th for Application of Integrals ( Exercise 8.1, 8.2, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles
 Exercise 8.1 Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 Question 13
 Exercise 8.2 Question 1 Question 2 Question 3 Question 4 Question 5 Question 6
 Exercise Miscellaneous Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 Question 13 Question 14 Question 15 Question 16 Question 17 Question 18