Applications of Integrals (Area): JEE Questions & Solutions

The area of the region, inside the ellipse x^2+4y^2=4 and outside the region bounded by the curves y=x-1 and y=1-x, is:

If the area of the region (x, y): 1 - 2x y 4 - x^2, x 0, y 0 is,, N, (,) = 1, then the value of ( +) is:

Let the line x = -1 divide the area of the region (x,y): 1 + x^2 y 3 - x in the ratio m:n, where (m,n)=1. Then m+n is equal to

The area of the region A = (x,y): 4x^2 + y^2 8 and y^2 4x is

Let the area of the region bounded by the curve y = x, x, lines x = 0, x = 3 /2, and the x-axis be A. Then, A + A^2 is equal to:

The area of the region enclosed between the circles x^2 + y^2 = 4 and x^2 + (y - 2)^2 = 4 is:

Let A1 be the bounded area enclosed by the curves y=x^2+2, x+y=8 and y-axis that lies in the first quadrant. Let A2 be the bounded area…

Let f() denote the area of the region in the first quadrant bounded by x=0, x=1, y^2=x and y=| x-5|-|1- x|+ ^2. Then (f(0)+f(1)) is equal to

The area of the region R= (x,y): xy 8, 1 y x^2, x 0 is:

Let P1: y = 4x^2 and P2: y = x^2 + 27 be two parabolas. If the area of the bounded region enclosed between P1 and P2 is six times the area…

The area of the region, inside the circle (x-2 3)^2 + y^2 = 12 and outside the parabola y^2 = 2 3x is:

The area of the region enclosed by the curves y = x^2 - 4x + 4 and y^2 = 16 - 8x is:

SECTION- B If the area of the larger portion bounded between the curves x^2 + y^2 = 25 and y = |x - 1| is 14(b + c), where b, c N, then b +…

If the area of the region (x, y): -1 x 1, 0 y a + e^|x| - e^-x, a 0 is e^2 + 8e + 1e, then the value of a is:

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm, the…

The area of the region (x, y): x^2 + 4x + 2 y |x| + 2 is equal to:

The area of the region enclosed by the curves y = e^x, y = |e^x - 1|, and the y-axis is:

The area (in sq. units) of the region (x, y): 0 y 2|x| + 1, 0 y x^2 + 1, |x| 3 is:

The area of the region bounded by the curves x(1 + y^2) = 1 and y^2 = 2x is:

Let the area of the region (x, y): 2y x^2 + 3, y + |x| 3, y |x-1| be A. Then 6A is equal to:

Let the area enclosed between the curves |y| = 1 - x^2 and x^2 + y^2 = 1 be. If 9 = +;, are integers, then the value of | - | equals:

If the area of the region (x, y): |4 - x^2| y x^2, y 0 is 80 2 -,, N, then + is equal to:

The area of the region bounded by the curve y = |x|, |x-2|, then x-axis and the lines x = -2 and x = 4 is equal to.

The area of the region (x, y): |x - y| y 4 x is

If the area of the region (x, y): |x - 5| y 4 x is A, then 3A is equal to

If the area of the region bounded by the curves y = 4 - x^24 and y = x - 42 is equal to, then 6 equals:

If the area of the region (x, y): 1 + x^2 y (x + 7, 11 - 3x) is A, then 3A is equal to:

Let the area of the bounded region (x, y): 0 9x y^2, y 3x - 6 be A. Then 6A is equal to:

Let the area of region (x,y): x - 2y + 4 0, x + 2y^2 0, x+4y^2 8, y 0 be m/n with m and n coprime. Find m+n.

If the area of the region (x, y): 0 y (2x, 6x - x^2) is A, then 12A is equal to:

Let the area of the region (x, y): 0 x 3, 0 y (x^2 + 2, 2x + 2) be A. Then 12A is equal to:

The area (in square units) of the region bounded by the parabola y^2 = 4(x - 2) and the line y = 2x - 8 is:

The area of the region defined by y^2 4x, x < 4, and xy(x - 1)(x - 2)(x - 3)(x - 4) 0 is:

Let S = (-1,) and f: S R be defined as: f(x) = -1^x (e^t - 1)^11 (2t - 1)^5 (t - 2)^7 (t - 3)^12 (2t - 10)^61 dt Let p be the sum of…

The area enclosed by the curves xy + 4y = 16 and x + y = 6 is equal to:

The area of the region (x, y): y^2 2x, y 4x - 1 is:

If the area of the region bounded by the curves y^2 - 2y = -x and x + y = 0 is A, then 8A is equal to:

It the area enclosed by the parabolas P1: 2y = 5x^2 and P2: x^2 - y + 6 = 0 is equal to the area enclosed by P1 and y = x, 0, then ^3 is…

Let A = (x, y) ∈ R^2: y 0, 2x y /4 - (x - 1)^2) B = (x, y) ∈ R^2: 0 y 2x, /4 - (x - 1)^2). Then the ratio of the area of A to the area of B…

Let be the area of the region (x, y) R^2: x^2 + y^2 21, y^2 4x, x 1. Then ( 12) - 21 ^-1 ( 2 7) is equal to:

The area of the region A = (x, y): | x - x| y x, 0 x 2 is:

Let be the area of the larger region bounded by the curve y^2 = 8x and the lines y = x and x = 2, which lies in the first quadrant. Then…

Let q be the maximum integral value of p in [0, 10] for which the roots of the equation x^2 - px + 5p4 = 0 are rational. Then the area of…

Let A be the area of the region (x, y): y x^2, y (1 - x)^2, y 2x(1 - x).Then 540A is equal to.....

Let the area of the region (x, y): |2x - 1| y x^2 - x, 0 x 1 be A. Then (6A + 11)^2 is equal to:

Let A be the area bounded by the curve y = x|x - 3| the x-axis, and the ordinates x = -1 and x = 2. Then 12A is equal to:

The area of the region given by (x, y): xy 8, 1 y x^2 is:

If the area of the region S = (x,y): 2y - y^2 x 2y, x y is equal to (1 - 1n) 4, then the natural number n is equal to:

The area bounded by the curves y = |x - 1| + |x - 2| and y = 3 is equal to:

The area of the region (x, y): x^2 y 8-x^2, y 7 is:

If y = p(x) is the parabola passing through points (-1, 0), (0, 1), and (1, 0), and the area of the region (x, y): (x + 1)^2 + (y - 1)^2 1,…

If A is the area in the first quadrant enclosed by the curve C: 2x^2 - y + 1 = 0, the tangent to C at the point (1, 3), and the line x + y…

The area of the region enclosed by the curve y = x^3 and its tangent at the point (-1, -1) is:

The area of the region enclosed by the curve f(x) = x, x, where - x and the x-axis is:

JEE Main 2023 Mathematics Questions with Solutions Section – A The area of the region (x,y): x^2 y |x^2 - 4|, y 1 is:

If the area bounded by the curve 2y^2=3x, the lines x+y=3, y=0 and lying outside the circle (x-3)^2+y^2=2 is A, then 4( +4A) is equal to