JEE Advanced Applications of Integrals — previous year questions

22 questions from 2025, 2024, 2023, 2022, 2021, 2020, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2009, 2008.

• Let R denote the set of all real numbers. Then the area of the region {(x, y) ∈ R × R : x > 0, y > 1/x, 5x -…2025JEE Advanced
• Let S denote the locus of the mid-points of those chords of the parabola y² = x, such that the area of the…2025JEE Advanced
• Let S={(x,y)∈R×R:x≥ 0, y≥ 0, y²≤ 4x, y²≤ 12-2x and 3y+√(8x)≤ 5√8}. If the area of the region S is a√2, then α…2024JEE Advanced
• Let f : [0,1] → [0,1] be the function defined by f(x) = x³/3 - x² + 5/9x + 17/36 . Consider the square region…2023JEE Advanced
• Let n ≥ 2 be a natural number and f: [0, 1] → R be the function defined by f(x) = n(1-2nx) if 0 ≤ x ≤ 1/2n…2023JEE Advanced
• Consider the functions f, g : R → R defined by f(x) = x² + 5/12 and g(x) = 2(1 - 4|x|/3), |x| ≤ 3/4, 0, |x| >…2022JEE Advanced
• The area of the region {(x,y): 0 ≤ x ≤ 9/4, 0 ≤ y ≤ 1, x ≥ 3y, x + y ≥ 2} is2021JEE Advanced
• Let the functions f:R → R and g:R → R be defined by f(x) = eˣ⁻¹ - e^(-|x-1|) and g(x) = 1/2(eˣ⁻¹ + e¹⁻ˣ).…2020JEE Advanced
• Let g(x) = cos x², f(x) = √x, and α, β (α < β) be the roots of the quadratic equation 18x² - 9π x + π² = 0.…2018JEE Advanced
• The area of the region {(x,y):xy ≤ 8, 1 ≤ y ≤ x²} is (1) 8logₑ2-14/3 (2) 16logₑ2-14/3 (3) 8logₑ2-7/3 (4)…2018JEE Advanced
• A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this…2018JEE Advanced
• If the line sx = alpha divides the area of region R = {(x,y) in R^2 : x^3 <= y <= x, 0 <= x <= 1} into two…2017JEE Advanced
• Area of the region {(x,y)∈R²: y≥√(|x+3|), 5y≤ x+9≤ 15} is equal to (1) 1/6 (2) 4/3 (3) 3/2 (4) 5/32016JEE Advanced
• Let F(x) = integral_x^{x^2 + pi/6} 2 cos^2 t dt for all x in R and f : [0, 1/2] -> [0, inf) be a continuous…2015JEE Advanced
• The area of the region described by A = {(x, y): x^2 + y^2 <= 1 and y^2 <= 1 - x} is: (1) pi/2 - 2/3 (2) pi/2…2014JEE Advanced
• The area enclosed by the curves y = sin x + cos x and y = |cos x − sin x| over the interval [0, π/2] is (1)…2013JEE Advanced
• Let S be the area of the region enclosed by y=e^(-x²), y=0, x=0 and x=1; then2012JEE Advanced
• Let f:[-1,2]→[0,∞) be a continuous function such that f(x)=f(1-x) for all x∈[-1,2] Let R₁=∫₋₁² xf(x) dx, and…2011JEE Advanced
• Let the straight line x = b divide the area enclosed by y=(1-x)², y=0, and x=0 into two parts R₁ (0 ≤ x ≤ b)…2011JEE Advanced
• Area of the region bounded by the curve y = eˣ and lines x = 0 and y = e is2009JEE Advanced
• Let f be a non-negative function defined on the interval [0,1]. If integral_0^x sqrt(1-(f'(t))^2) dt =…2009JEE Advanced
• The area of the region between the curves y=√((1+sin x)/(cos x)) and y=√((1-sin x)/(cos x)) bounded by the…2008JEE Advanced

Practise these with video solutions