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

Application of Integrals Class 12

Chapter 8 Application of Integrals Exercise 8.1, 8.2, miscellaneous Solutions

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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.

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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.

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Q3 :  

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


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Q4 :  

Find the area of the region bounded by the ellipse


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Q5 :  

Find the area of the region bounded by the ellipse


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Q6 :  

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


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Q7 :  

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


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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.


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Q9 :  

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


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Q10 :  

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


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Q11 :  

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


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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.


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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.


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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


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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


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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).


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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.


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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)


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Q6 :  

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

A.

B.

C.

D.


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<< Previous Chapter 7 : Integrals Next Chapter 9 : Differential Equations >>

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


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Q2 :  

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


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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


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Q4 :  

Sketch the graph of and evaluate


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Q5 :  

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


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Q6 :  

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


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Q7 :  

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


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Q8 :  

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


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Q9 :  

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


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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


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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 – y = 1, – x + y = 1 and – x – y = 11]


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Q12 :  

Find the area bounded by curves


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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


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Q14 :  

Find the area of the region


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Q15 :  

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

A. – 9

B.

C.

D.


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Q16 :  

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

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

A. 0

B.

C.

D.


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Q17 :  

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

A.

B.

C.

D.


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Q18 :  

The area bounded by the y-axis, y = cos x and y = sin x when

A.

B.

C.

D.


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<< Previous Chapter 7 : Integrals Next Chapter 9 : Differential Equations >>

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.

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