Application of Integrals

CBSE Class 12 Mathematics · every board question from this chapter, 2022–2026

• Which of the following expressions will give the area of region bounded by the curve y=x^2 and line y=16?2026
• The area bounded by the curve y=x|x|, x -axis and the ordinates x=-1 and x=1 is given by2026
• The area of the region bounded by the curve y=x and x -axis, between x=0 and x=2 is:2026
• An ant is observed crawling on a sheet of paper along a straight line given by equation y=2 x-4. Area of the surface covered by…2026
• The area of the shaded region of the circle given below is equal to:2026
• Using integration, find the area of the region bounded by y=5 x+4, y=0, x=-1 and x=1.2026
• Using integration, find the area of the region enclosed by the curve y=|x-6|, the x -axis, and between x=4 and x=8.2026
• Using integration, find the area of the region bounded by the curve y=x|x|, x -axis, x=-2 and x=2.2026
• Sketch the curve described by {(x, y): 9 x^2+16 y^2=144} and find the area of the region enclosed by it, using integration.2026
• Sketch the curve {(x, y): 100 x^2+25 y^2=2500} and find the area of the region enclosed by it, using integration.2026
• Sketch the graph defined by {(x, y): (x^2)/25+(y^2)/25=1}. Find the area of the region of minor segment cut off by the line…2026
• There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC,…2026
• A racing track is build around an elliptical ground whose equation is given by 9 x^2+16 y^2=144. The width of the track is 3 m as…2026
• Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that…2026
• The following graph is a combination of:2025
• The area of the region enclosed between the curve y=x|x|, x -axis, x=-2 and x=2 is:2025
• The area of the shaded region (figure) represented by the curves y=x^2, 0 ≤ x ≤ 2 and y -axis is given by2025
• The area of the region bounded by the curve y^2=x between x=0 and x=1 is:2025
• The area of the region enclosed by the curve y=√x and the lines x=0 and x=4 and x -axis is:2025
• The area of the shaded region bounded by the curves y^2=x, x=4 and the x -axis is given by2025
• Calculate the area of the region bounded by the curve (x^2)/9+(y^2)/4=1 and the x -axis using integration.2025
• Sketch the graph of y=|x+3| and find the area of the region enclosed by the curve, x -axis, between x=-6 and x=0, using…2025
• Using integration, find the area of the region bounded by the line y=5 x+2, the x -axis and the ordinates x=-2 and x=2.2025
• In a rough sketch, mark the region bounded by y=1+|x+1|, x=-2, x=2 and y=0. Using integration, find the area of the marked region.2025
• Sketch a graph of y=x^2. Using integration, find the area of the region bounded by y=9, x=0 and y=x^2.2025
• Draw a rough sketch of the curve y=√x. Using integration, find the area of the region bounded by the curve y=√x, x=4 and x -axis,…2025
• Use integration to find the area of the region enclosed by curve y=-x^2 and the straight lines x=-3, x=2 and y=0. Sketch a rough…2025
• Using integration, find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 bounded between the lines x=-a/2 to x=a/2.2025
• Draw a rough sketch for the curve y=2+|x+1|. Using integration, find the area of the region bounded by the curve y=2+|x+1|, x=-4,…2025
• A woman discovered a scratch along a straight line on a circular table top of radius 8 cm. She divided the table top into 4 equal…2025
• The area bounded by the curve y=√x, Y -axis and between the lines y=0 and y=3 is:2024
• The area of the region bounded by the curve y^2=4 x and x=1 is:2024
• Area of the region bounded by curve y^2=4 x and the X -axis between x=0 and x=1 is:2024
• Sketch the graph of y=x|x| and hence find the area bounded by this curve, X -axis and the ordinates x=-2 and x=2, using…2024
• Find the area of the region bounded by the lines x-2 y=4, x=-1, x=6 and x -axis, using integration.2024
• Find the area of the region bounded by the curve 4 x^2+y^2=36 using integration.2024
• Using integration, find the area of the region enclosed between the circle x^2+y^2=16 and the lines x=-2 and x=2.2024
• Using integration, find the area of the ellipse (x^2)/16+(y^2)/4=1, included between the lines x=-2 and x=2.2024
• Using integration, find the area of the region enclosed between the curve y=√(4-x^2) and the lines x=-1, x=1 and the x -axis.2024
• If A_1 denotes the area of region bounded by y^2=4 x, x=1 and x -axis in the first quadrant and A_2 denotes the area of region…2024
• Sketch the region bounded by the lines 2 x+y=8, y=2, y=4 and the y -axis. Hence, obtain its area using integration.2023
• Using integration, find the area of the region bounded by y=m x( m>0), x=1, x=2 and the x -axis.2023
• Find the area of the following region using integration: {(x, y): y^2 ≤ 2 x and y ≥ x-4}2023
• Find the area of the minor segment of the circle x^2+y^2=4 cut off by the line x=1, using integration.2023
• Using integration, find the area of the region bounded by the circle x^2+y^2=16, line y=x and y -axis, but lying in the 1^st…2023
• Find the area of the region {(x, y): x^2+y^2 ≤ 1 ≤ x+y}, using integration.2023
• Using integration, find the area of the region bounded by the parabola y^2=4 a x and its latus rectum.2023
• The area of the region bounded by the line y=mx(m>0), the curve x^2+y^2=4 and the x -axis in the first quadrant is (π)/2 units.…2023
• Using Integration, find the area of triangle whose vertices are ( -1,1 ), (0,5) and (3,2).2023
• Find the area of the region bounded by the lines y=4 x+5, x+y=5 and 4 y=x+5, using integration.2023
• Using integration, find the area of region bounded by line y=√3 x, the curve y=√(4-x^2) and y -axis in first quadrant.2023
• Find the area of the smaller region bounded by the curves (x^2)/25+(y^2)/16=1 and x/5+y/4=1, using integration.2023
• Find the area of the region bounded by the curves x^2=y, y=x+2 and x-axis, using integration.2023
• Find the area of the region {(x, y): x^2 ≤ y ≤ x+2}, using integration.2022
• Using integration, find the area of the region {(x, y): y^2 ≤ x ≤ y}.2022
• If the area of the region bounded by the line y=mx and the curve x^2=y is 32/3 sq. units, then find the positive value of m,…2022
• Using integration, find the area of the smaller region enclosed by the curve 4 x^2+4 y^2=9 and the line 2 x+2 y=3. OR If the area…2022
• Find the area of the region bounded by curve 4 x^2=y and the line y=8 x+12, using integration.2022
• Using integration, find the area of the region {(x, y): 4 x^2+9 y^2 ≤ 36., 2 x+3 y ≥ 6}. OR Using integration, find the area of…2022
• Using integration, find the area of the region bounded by the curves x^2+y^2=4, x=√3 y and x -axis lying in the first quadrant.2022
• Find the area bounded by the curves y=|x-1| and y=1, using integration.2022
• Using integration, find the area of the region enclosed by the curve y=x^2, the x -axis and the ordinates x=-2 and x=1. OR Using…2022
• Find the area of the region enclosed by the curves y^2=x, x=1/4, y=0 and x=1, using integration. Case Study Problem:2022

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