Area Between Two or More Curves

JEE Main Mathematics · Area Under the Curve · 69 questions, latest first

• Let f:(1, ∞) → R be a function defined as f(x)=(x-1)/(x+1). Let f^i+1(x)=f(f^i(x)), i=1,2, …, 25, where f^1(x)=f(x). If…20268 April, Shift 2 · Q18
• The area of the region {(x, y): x^2-8 x ≤ y ≤-x} is:20266 April, Shift 2 · Q19
• The area of the region {(x, y): 0 ≤ y ≤ 6-x, y^2 ≥ 4 x-3, x ≥ 0} is:20266 April, Shift 1 · Q19
• Let e be the base of natural logarithm and let f:{1,2,3,4} →{1, e, e^2, e^3} and g:{1, e, e^2, e^3} →{1, 1/2, 1/3, 1/4} be two…20266 April, Shift 1 · Q20
• Let f: R → R be a function such that f(x)+3 f((π)/2-x)= sin x, x ∈ R. Let the maximum value of f on R be α. If the area of the…20265 April, Shift 2 · Q24
• The area of the region R={(x, y): x y ≤ 27,1 ≤ y ≤ x^2} is equal to:20265 April, Shift 1 · Q16
• The area of the region bounded by the curves x+3 y^2=0 and x+4 y^2=1 is equal to:20264 April, Shift 2 · Q18
• The area of the region {(x, y): y ≤ π-|x|, y ≤|x sin x|, y ≥ 0} is:20264 April, Shift 1 · Q18
• If the area of the region bounded by 16 x^2-9 y^2=144 and 8 x-3 y=24 is A, then 3( A+6 log_e(3)) is equal to ____.20262 April, Shift 2 · Q24
• Let P_1: y=4 x^2 and P_2: y=x^2+27 be two parabolas. If the area of the bounded region enclosed between P_1 and P_2 is six times…202628 January, Shift 2 · Q20
• The area of the region R={(x, y): x y ≤ 8,1 ≤ y ≤ x^2, x ≥ 0} is202628 January, Shift 1 · Q17
• Let f(α) denote the area of the region in the first quadrant bounded by x=0, x=1, y^2=x and y=|α x-5|-|1-α x|+α x^2. Then…202624 January, Shift 2 · Q19
• Let A_1 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 A_2 be the…202624 January, Shift 1 · Q20
• The area of the region A={(x, y): 4 x^2+y^2 ≤ 8. and.y^2 ≤ 4 x} is:202622 January, Shift 2 · Q19
• Let the line x=-1 divide the area of the region {(x, y): 1+x^2 ≤ y ≤ 3-x} in the ratio m: n, gcd(m, n)=1. Then m+n is equal to202622 January, Shift 1 · Q18
• If the area of the region {(x, y): 1-2 x ≤ y ≤ 4-x^2, x ≥ 0, y ≥ 0} is (α)/(β), α, β ∈ N, gcd(α, β)=1, then the value of (α+β) is:202621 January, Shift 2 · Q20
• Let the area of the bounded region {(x, y): 0 ≤ 9 x ≤ y^2, y ≥ 3 x-6} be A. Then 6 A is equal to ____20258 April, Shift 2 · Q25
• If the area of the region {(x, y): 1+x^2 ≤ y ≤ min {x+7,11-3 x}} is A, then 3 A is equal to20257 April, Shift 2 · Q20
• If the area of the region bounded by the curves y=4-x^2/4 and y=(x-4)/2 is equal to α, then 6 α equals20257 April, Shift 1 · Q19
• A line passing through the point A(-2,0), touches the parabola P: y^2=x-2 at the point B in the first quadrant. The area, of the…20254 April, Shift 2 · Q19
• If the area of the region {(x, y):|x-5| ≤ y ≤ 4 √x} is A, then 3 A is equal to ____20254 April, Shift 1 · Q25
• The area of the region {(x, y):|x-y| ≤ y ≤ 4 √x} is20253 April, Shift 2 · Q19
• If the area of the region {(x, y):|4-x^2| ≤ y ≤ x^2, y ≤ 4, x ≥ 0} is ((80 √2)/(α)-β), α, β ∈ N, then α+β is equal to ____.20252 April, Shift 1 · Q21
• Let the area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 be α. If 9 α=β π+γ; β, γ are integers, then the value of |β-γ|…202529 January, Shift 2 · Q19
• Let the area of the region {(x, y): 2 y ≤ x^2+3, y+|x| ≤ 3, y ≥|x-1|} be A. Then 6 A is equal to:202529 January, Shift 1 · Q19
• The area of the region bounded by the curves x(1+y^2)=1 and y^2=2 x is:202528 January, Shift 2 · Q20
• The area (in sq. units) of the region {(x, y): 0 ≤ y ≤ 2|x|+1,0 ≤ y ≤ x^2+1,|x| ≤ 3} is202528 January, Shift 1 · Q17
• The area of the region enclosed by the curves y=e^x, y=|e^x-1| and y -axis is:202524 January, Shift 2 · Q19
• The area of the region {(x, y): x^2+4 x+2 ≤ y ≤|x+2|} is equal to202524 January, Shift 1 · Q19
• The area of the region enclosed by the curves y=x^2-4 x+4 and y^2=16-8 x is:202522 January, Shift 2 · Q18
• The area of the region, inside the circle (x-2 √3)^2+y^2=12 and outside the parabola y^2=2 √3 x is:202522 January, Shift 1 · Q19
• Let the function, f(x)= {-3 a x^2-2, x<1; a^2+b x, x ≥ 1} be differentiable for all x ∈ R, where a>1, b ∈ R. If the area of the…202522 January, Shift 1 · Q25
• The parabola y^2=4 x divides the area of the circle x^2+y^2=5 in two parts. The area of the smaller part is equal to:20249 April, Shift 1 · Q9
• The area of the region in the first quadrant inside the circle x^2+y^2=8 and outside the parabola y^2=2 x is equal to:20248 April, Shift 2 · Q12
• If the area of the region {(x, y): a/x^2 ≤ y ≤ 1/x, 1 ≤ x ≤ 2,0<a<1} is ( log_e 2)-1/7 then the value of 7 a-3 is equal to:20246 April, Shift 2 · Q11
• Let the area of the region enclosed by the curves y=3 x, 2 y=27-3 x and y=3 x-x √x be A. Then 10 A is equal to20246 April, Shift 1 · Q12
• The area enclosed between the curves y=x|x| and y=x-|x| is:20245 April, Shift 2 · Q12
• The area of the region enclosed by the parabolas y=x^2-5 x and y=7 x-x^2 is ____.20245 April, Shift 1 · Q27
• The area (in sq. units) of the region described by {(x, y): y^2 ≤ 2 x., and.y ≥ 4 x-1} is20244 April, Shift 2 · Q11
• One of the points of intersection of the curves y=1+3 x-2 x^2 and y=1/x is (1/2, 2). Let the area of the region enclosed by these…20244 April, Shift 1 · Q13
• The area enclosed by the curves x y+4 y=16 and x+y=6 is equal to:20241 February, Shift 1 · Q9
• The area of the region enclosed by the parabolas y=4 x-x^2 and 3 y=(x-4)^2 is equal to202431 January, Shift 2 · Q11
• The area of the region enclosed by the parabola (y-2)^2=x-1, the line x-2 y+4 =0 and the positive coordinate axes is ____.202430 January, Shift 2 · Q26
• The area (in square units) of the region bounded by the parabola y^2=4(x-2) and the line y=2 x-8, is:202430 January, Shift 1 · Q11
• Let the area of the region {(x, y): 0 ≤ x ≤ 3,0 ≤ y ≤ min {x^2+2,2 x+2}} be A. Then 12 A is equal to ____.202429 January, Shift 2 · Q27
• If the area of the region {(x, y): 0 ≤ y ≤ min {2 x, 6 x-x^2}} is A, then 12 A is equal to ____.202427 January, Shift 2 · Q26
• Let the area of the region {(x, y): x-2 y+4 ≥ 0, x+2 y^2 ≥ 0, x+4 y^2 ≤ 8, y ≥ 0} be m/n, where m and n are coprime numbers. Then…202427 January, Shift 1 · Q26
• If the area bounded by the curve 2 y^2=3 x, lines x+y=3, y=0 and outside the circle (x-3)^2+y^2=2 is A, then 4(π+4 A) is equal to…202315 April, Shift 1 · Q27
• The area of the region {(x, y): x^2 ≤ y ≤|x^2-4|, y ≥ 1} is202313 April, Shift 2 · Q11
• The area of the region enclosed by the curve y=x^3 and its tangent at the point ( -1,-1 ) is202312 April, Shift 1 · Q10
• If A is the area in the first quadrant enclosed by the curve C: 2 x^2-y+1=0, the tangent to C at the point (1,3) and the line…202311 April, Shift 2 · Q25
• Area of the region {(x, y): x^2+(y-2)^2 ≤ 4, x^2 ≥ 2 y} is202311 April, Shift 1 · Q9
• If the area of the region {(x, y):|x^2-2| ≤ y ≤ x} is A, then 6 A+16 √2 is equal to ____.202310 April, Shift 2 · Q26
• Let y=p(x) be the parabola passing through the points (-1,0),(0,1) and (1,0). If the area of the region {(x, y):(x+1)^2+(y-1)^2 ≤…202310 April, Shift 1 · Q28
• Let the area enclosed by the lines x+y=2, y=0, x=0 and the curve f(x)= min {x^2+3/4, 1+[x]} where [x] denotes the greatest…20238 April, Shift 2 · Q27
• The area of the region {(x, y): x^2 ≤ y ≤ 8-x^2, y ≤ 7} is20238 April, Shift 1 · Q12
• The area bounded by the curves y=|x-1|+|x-2| and y=3 is equal to20236 April, Shift 2 · Q14
• If the area of the region S={(x, y): 2 y-y^2 ≤ x^2 ≤ 2 y, x ≥ y} is equal to (n+2)/(n+1)-(π)/(n-1), then the natural number n is…20236 April, Shift 1 · Q26
• The area of the region given by {(x, y): x y ≤ 8,1 ≤ y ≤ x^2} is:20231 February, Shift 2 · Q71
• Let the area of the region {(x, y):|2 x-1| ≤ y ≤|x^2-x|, 0 ≤ x ≤ 1} be A. Then (6 A+11)^2 is equal to ____.202331 January, Shift 2 · Q86
• Let for x ∈ R, f(x)=(x+|x|)/2 and g(x)= {x, x<0; x^2, x ≥ 0}. Then area bounded by the curve y=(f ° g)(x) and the lines y=0,2…202331 January, Shift 1 · Q86
• Let A be the area of the region {(x, y): y ≥ x^2, y ≥(1-x)^2, y ≤ 2 x(1-x)}. Then 540 A is equal to ____.202330 January, Shift 2 · Q86
• Let α be the area of the larger region bounded by the curve y^2=8 x and the lines y=x and x=2, which lies in the first quadrant.…202330 January, Shift 1 · Q90
• The area of the region A={(x, y):| cos x- sin x| ≤ y ≤ sin x, 0 ≤ x ≤ (π)/2} is202329 January, Shift 2 · Q69
• Let Δ be the area of the region {(x, y) ∈ R^2: x^2+y^2 ≤ 21, y^2 ≤ 4 x, x ≥ 1}. Then 1/2(Δ-21 sin^-1 2/(√7)) is equal to202329 January, Shift 1 · Q70
• Let T and C respectively be the transverse and conjugate axes of the hyperbola 16 x^2-y^2+64 x+4 y +44=0. Then the area of the…202325 January, Shift 2 · Q74
• It the area enclosed by the parabolas P_1: 2 y=5 x^2 and P_2: x^2-y+6=0 is equal to the area enclosed by P_1 and y=α x, α>0, then…202325 January, Shift 1 · Q88
• If the area of the region bounded by the curves y^2-2 y=-x, x+y=0 is A, then 8 A is equal to ____202324 January, Shift 2 · Q84
• The area enclosed by the curves y^2+4 x=4 and y-2 x=2 is:202324 January, Shift 1 · Q75