NCERT Solutions for Class 12 Chapter 8 Application of Integral

NCERT Solutions for Class 12 Chapter 8 Application of Integral

Exercise 8.1

• 1   Find the area of the region bounded by the curve y^2 =x and the lines x = 1 , x = 4 and the x axis 2   Find the area of the region bounded by y^2 = 9x, x=2, x =4 and the x axis in the first quadrant 3   How to area bounded by hyperbola and lines x^2 = 4y , y=2, y=4 and the y axis in the first quadrant 4   Bounded area of ellipse: Find the equation of the region bounded by the ellipse x^2/16 + y^2/9 =1 5   Application of integrals: Find the equation of the region bounded by the ellipse x^2/4 + y^2/9 =1 6   Application of Integrals:How to find the area of the region in the first quadrant enclosed 8   Area between x=y2 and x=4 is divided in two equal parts by the line x = a, find the value of a 9   Find the area of the region bounded by the parabola y = x^2 and y= |x| 10   Find the area bounded by the curve x^2 =4y and the line x = 4y- 2 12   Area lying in the first quadrant and bounded by the circle x^2 + y^2 =4 and lines x =0 and x = 2 13   Area of the region bounded by the curve y^2 =4x , y axis and the line y=3 is Exercise 8.2 1   Find the area of the circle 4x^2 + 4y^2 = 9 which is interior to the parabola x^2 =4y 2   Find the area bounded by curves (x – 1)^2 + y^2 = 1 and x^2 + y^2 = 1 3   Find the area of the region bounded by the curves y= x^2 + 2 , y=x , x =0 and x = 3 4   Using integration find the area of region bounded by the triangle whose vertices are ... 5   Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, 6   Smaller area enclosed by the circle x^2 +y^2 = 4 and the lines x + y = 2 is 7   Area lying between the curves y^2 = 4x and y = 2x is Miscellaneous Exercise Questions Solution 1   Find the area under the given curves and given lines y = x^2 , x=1 , x= 2 and x axis 2   Application of integrals: Find the area between the curves y = x and y = x^2 3   Find the area of the region lying in the first quadrant and bounded by y = 4x^2, x=0, y=1 and y= 4 4   Sketch the graph of y = x + 3 and evaluate integration limits 6 to 0 of x + 3 dx 5   Find the area bounded by the curve y = sin x between x = 0 and x = 2π 6   Bunded area region : Find the area enclosed between the parabola y^2 = 4ax and the line y =mx 7   Find the area enclosed by the parabola 4y = 3x^2 and the line 2y = 3x + 12 8   Find the area of the smaller region bounded by the ellipse x^2/9 + y^2/4 = 1 and the line 10   Find the area of the region enclosed by the parabola x^2 = y, the line y = x + 2 and the x axis 11   Using the method of integration find the area bounded by the curve 12   Find the area bounded by curves {x, y y ≥ x^2 and y =| x| 13   Using the method of integration find the area of the triangle ABC, coordinates of whose vertices 14   Using the method of integration find the area of the region bounded by lines 2x + y = 4, 3x – 2y = 6 15   Find the area of the region {x, y y^2 = 4x, 4x^2 + 4y^2 = 9} 16   Area bounded by the curve y = x^3, the x axis and the ordinates x = – 2 and x = 1 is 17   The area bounded by the curve y = x|x|, x axis and the ordinates x = – 1 and x = 1 is given by Ex -14   the area of the region {x, y : 0 ≤ y ≤ x^2 + 1, 0 ≤ y ≤ x + 1, 0 ≤ x ≤ 2} Ex12   Find the area of the region bounded by the line y = 3x + 2, the x axis and the ordinates x = –1 and 19   The area bounded by the y axis, y = cos x and y = sin x when 0 ≤ x ≤ π2