Integrals

CBSE Class 12 Mathematics · 190 board questions from this chapter; 187 listed below, 2022–2026 · 1 of them repeated across years

• If ∫ (3 a x)/(b^2+c^2 x^2) d x=A log |b^2+c^2 x^2|+K, then the value of A is2026
• ∫ (d x)/(1+ cos x) is equal to2026
• ∫ dx/(√(e^-2 x-1)) is equal to:2026
• If ∫_0^2 a 1/(1+4 x^2) d x=(π)/6, then the value of a is2026
• The value of ∫_-1^1 (x^3)/(x^2+2|x|+1) d x is2026
• ∫ dx/(√(25-16 x^2)) is equal to:2026
• ∫ 1/(√(1+ cos 2 x)) dx is equal to:2026
• ∫ √((1- cos 2 x)/(1+ cos 2 x)) dx is equal to:2026
• If ∫_0^1 dx/(e^x+e^-x)= tan^-1 e+k, then the value of k is:2026
• ∫ dx/(2^x+2^-x) is equal to:2026
• ∫ √((1+ cos x)/(1- cos x)) dx is equal to:2026
• The value of ∫_0^1 1/(3 x-4) dx is:2026
• ∫_-1^1(1-|x|) dx is equal to:2026
• The value of ∫_-5^-1 1/x dx is equal to:2026
• If ∫_0^1(6 x^2-4 x+k) dx=0, then the value of k is:2026
• ∫ (d x)/(sec x+ tan x) is equal to2026
• ∫ (cos x)/(√(sin^2 x+1)) dx is equal to:2026
• Find: ∫ (x+2)/(√(9 x-x^2)) d x2026
• Evaluate: ∫_0^1 log (1+x^2) d x2026
• Find: ∫ (d x)/(x^1 / 2+x^1 / 3) OR Find: ∫ tan^-1((1-x)/(1+x)) d x2026
• Evaluate: ∫_0^1 x tan^-1 x d x.2026
• Evaluate: ∫_0^π (sin^2026 x)/(sin^2026 x+ cos^2026 x) d x2026
• Find ∫ √((x+2)/(x-2)) d x OR Find: ∫ (x^2)/((x^2+9)(x^2+16)) d x2026
• Evaluate: ∫_((π)/12)^((5 π)/12) (d x)/(1+√(cot x)) OR Evaluate: ∫_((-π)/6)^((π)/2)( sin |x|+ cos |x|) d x2026
• Find: ∫ (x- sin x)/(1- cos x) d x OR Evaluate: ∫_0^2 1/(√(x^2+2 x+3)) d x2026
• Find: ∫ (3 x-1)/(√(x^2-4 x)) d x2026
• Evaluate: ∫_0^((π)/2) (sin^2 x)/(1+ sin 2 x) d x2026
• If I_1=∫_-π / 4^π / 4 (d x)/(1+ cos 2 x) and I_2=∫_-1 / 2^1 / 2|x| d x, then show that I_1-4 I_2=0.2026
• If d/(d x)( F(x))=1/(e^x+1), then find F(x) given that F(0)= log 1/2.2026
• Find: ∫ (cos x)/((2+ sin x)(4+ sin x)) d x OR Find: ∫ (x+3)/(x^2+4 x+5) d x2026
• Evaluate: ∫_0^1 x sin^-1 x d x2026
• Find: ∫ (2 x+1)/(√(6 x+x^2)) d x2026
• Evaluate: ∫_-(π)/2^((π)/2) (cos^2 x)/(2^x+1) d x2026
• Find: ∫ x/((x-1)(x^2+4)) dx OR Evaluate: ∫_0^1 (x tan^-1 x)/((1+x^2)^3 / 2) d x2026
• If ∫_0^1 (e^x)/(1+x) d x=α, then ∫_0^1 (e^x)/((1+x)^2) d x is equal to2025
• If f(2 a-x)=f(x), then ∫_0^2 a f(x) d x is2025
• ∫_-1^1 (|x|)/x d x, x ≠ 0 is equal to2025
• ∫ (1-2 sin x)/(cos^2 x) d x is equal to:2025
• ∫ (d x)/(sin^2 x cos^2 x) is equal to2025
• If ∫_0^a x d x ≤ a/2+6, then2025
• If ∫ (2^(1/x))/(x^2) d x=k · 2^(1/x)+C, then k is equal to2025
• ∫ √(1+ sin x) dx is equal to:2025
• ∫ (cos 2 x)/(sin^2 x cos^2 x) dx is equal to:2025
• ∫ (e^9 log x-e^8 log x)/(e^6 log x-e^5 log x) dx is equal to:2025
• If ∫_0^a 1/(1+4 x^2) dx=(π)/8, then the value of 'a' is:2025
• ∫_0^π / 2 cos x · e^sin x dx is equal to:2025
• ∫_0^1 (2 x)/(5 x^2+1) dx is equal to:2025
• ∫ (e^-x)/(16+9 e^-2 x) dx is equal to:2025
• ∫ (cos 2 x- cos 2 α)/(cos x- cos α) d x is equal to:2025
• ∫ (e^x)/(√(4-e^2 x)) dx is equal to:2025
• ∫ (a^x)/(√(1-a^2 x)) dx is equal to:2025
• ∫ e^x( cos x- sin x) dx is equal to:2025
• If ∫ e^-3 log x dx=f(x)+C, then f(x) is:2025
• The value of ∫_0^1 (d x)/(e^x+e^-x) is:2025
• ∫ (x+5)/((x+6)^2) e^x dx is equal to:2025
• Evaluate: ∫_0^π (sin 2 p x)/(sin x) d x, p ∈ N.2025
• Evaluate: ∫_0^((π)/4) √(1+ sin 2 x) d x2025
• Find: ∫ 2 x^3 e^x^2 d x.2025
• Find: ∫ (√x)/(1+√(x^3 / 2)) d x2025
• Find: ∫ (2 x)/((x^2+3)(x^2-5)) d x OR Evaluate: ∫_1^4(|x-2|+|x-4|) d x2025
• Find: ∫ (2 x-1)/((x-1)(x+2)(x-3)) d x OR Evaluate: ∫_0^5(|x-1|+|x-2|+|x-5|) d x2025
• Find: ∫ (cos x d x)/(1+ cos x+ sin x)2025
• Find: ∫ (x+ sin x)/(1+ cos x) d x OR Evaluate: ∫_0^((π)/4) (d x)/(cos^3 x √(2 sin 2 x))2025
• Evaluate: ∫_π / 2^π e^x((1- sin x)/(1- cos x)) d x2025
• Find: ∫ (cos 2 x)/(( sin x+ cos x)^2) d x OR Evaluate: ∫_0^((π)/2) (5 sin x+3 cos x)/(sin x+ cos x) d x2025
• Find: ∫ 1/x √((x+a)/(x-a)) d x.2025
• f and g are continuous functions on interval [a, b]. Given that f(a-x)=f(x) and g(x)+g(a-x)=a, show that ∫_0^a f(x) g(x) d x=a/2…2025
• If ∫_a^b x^3 d x=0 and ∫_a^b x^2 d x=2/3, then find the values of a and b.2025
• Find: ∫ (x^2+1)/((x-1)^2(x+3)) d x OR Evaluate: ∫_0^π / 2 x/(sin x+ cos x) d x2025
• Find: ∫ x/((x-1)(x^2+4)) d x OR Evaluate: ∫_0^π (x sin x)/(1+ cos^2 x) d x2025
• Find: ∫ (x^2+1)/((x^2+2)(2 x^2+1)) d x OR Evaluate: ∫_0^π (x tan x)/(sec x+ tan x) d x2025
• Find: ∫ (3 x+1)/((x-2)^2(x+2)) d x OR Evaluate: ∫_0^π / 2 x/(cos x+ sin x) d x2025
• Find: ∫ (x^2+x+1)/((x+2)(x^2+1)) d x.2025
• Find: ∫ (5 x)/((x+1)(x^2+9)) d x.2025
• Find: ∫ sin^-1 √(x/(a+x)) d x.2025
• Find: ∫(√(tan x)+√(cot x)) d x.2025
• Evaluate: ∫_0^π / 4 (sin x cos x)/(cos^4 x+ sin^4 x) d x OR Find: ∫ (√(x^2+1)[ log (x^2+1)-2 log x])/(x^2) d x2025
• Find: ∫ (cos x)/((4+ sin^2 x)(5-4 cos^2 x)) d x OR Evaluate: ∫_0^π (d x)/(a^2 cos^2 x+b^2 sin^2 x)2025
• Evaluate: ∫_0^3 / 2|x cos π x| d x Find: ∫ (d x)/(sin x+ sin 2 x)2025
• ∫_a^b f(x) d x is equal to:2024
• ∫_0^π / 2 (sin x- cos x)/(1+ sin x cos x) d x is equal to:2024
• ∫_-a^a f(x) d x=0, if:2024
• The value of ∫_0^π tan^2((θ)/3) d θ is:2024
• The value of ∫_-1^1|x| d x is:2024
• The value of ∫_0^3 (d x)/(√(9-x^2)) is:2024
• The value of ∫_π / 4^π / 2 cot θ cosec^2 θ d θ is:2024
• If ∫_-2^3 x^2 d x=k ∫_0^2 x^2 d x+∫_2^3 x^2 d x, then the value of k is:2024
• ∫ 1/(x( log x)^2) d x is equal to:2024
• Anti-derivative of √(1+ sin 2 x), x ∈[0, (π)/4] is:2024
• The value of ∫_-1^1 x|x| d x is:2024
• The value of ∫_1^e log x d x is:2024
• ∫_-a^a f(x) d x=0, if:2024
• The integral ∫ (d x)/(√(9-4 x^2)) is equal to:2024
• If f(x) is an odd function, then ∫_-π / 2^π / 2 f(x) cos^3 x d x equals:2024
• If ∫_0^2 2 e^2 x dx=∫_0^a e^x dx, the value of ' a ' is:2024
• If ∫_0^a 1/(4+x^2) dx=(π)/6, then the value of ' a ' is:2024
• Evaluate: ∫_0^a^3 (x^2)/(x^6+a^6) d x2024
• Evaluate: ∫_0^π / 2 sin 2 x cos 3 x d x OR Given d/(d x) F(x)=1/(√(2 x-x^2)) and F(1)=0, find F(x).2024
• Find: ∫ x √(1+2 x) dx; OR Evaluate: ∫_0^(π)/4^2 (sin √x)/(√x) d x2024
• Find: ∫ (e^4 x-1)/(e^4 x+1) d x2024
• Find: ∫ cos^3 x e^log sin x d x OR Find: ∫ 1/(5+4 x-x^2) d x2024
• Evaluate: ∫_(-1/2)^(1/2) cos x · log ((1+x)/(1-x)) d x2024
• Find: ∫ (2 x)/((x^2+1)(x^2-4)) d x.2024
• Find: ∫ 1/(x(x^2-1)) d x.2024
• Find: ∫ (x^-1)/(( log x)^2-5 log x+4) d x2024
• Evaluate: ∫_0^((π)/4) (x d x)/(1+ cos 2 x+ sin 2 x) OR Find: ∫ e^x[1/((1+x^2)^(3/2))+x/(√(1+x^2))] d x2024
• Find: ∫ x^2 log (x^2-1) d x2024
• Evaluate: ∫_-2^2 √((2-x)/(2+x)) dx; OR Find: ∫ 1/(x[( log x)^2-3 log x-4]) d x2024
• Find: ∫ (2 x+3)/(x^2(x+3)) d x2024
• Evaluate: ∫_0^π (e^cos x)/(e^cos x+e^- cos x) d x OR Find: ∫ (2 x+1)/((x+1)^2(x-1)) d x2024
• Find: ∫ (x^2)/((x^2+4)(x^2+9)) d x OR Evaluate: ∫_1^3(|x-1|+|x-2|+|x-3|) dx2024
• Find: ∫ (3 x+5)/(√(x^2+2 x+4)) d x2024
• Find: ∫ sec^3 θ d θ2024
• Find: ∫ (x^2+1)/((x^2+2)(x^2+4)) d x2024
• Find: ∫ (2+ sin 2 x)/(1+ cos 2 x) e^x d x OR Evaluate: ∫_0^π / 4 1/(sin x+ cos x) d x2024
• Find: ∫ (√x)/((x+1)(x-1)) d x2024
• Find: ∫ x^2 · sin^-1(x^3 / 2) d x2024
• Evaluate: ∫_0^π / 2 e^x((1+ sin x)/(1+ cos x)) d x OR Find: ∫_π / 6^π / 3 (sin x+ cos x)/(√(sin 2 x)) d x2024
• Evaluate: ∫_0^((π)/4) (sin x+ cos x)/(9+16 sin 2 x) dx; OR Evaluate: ∫_0^((π)/2) sin 2 x tan^-1( sin x) d x2024
• Find: ∫ ((3 cos x-2) sin x)/(5- sin^2 x-4 cos x) d x OR Evaluate: ∫_-2^2 (x^3+|x|+1)/(x^2+4|x|+4) d x2024
• ∫ (1+ tan x)/(1- tan x) dx is equal to:2023
• If ∫_0^2 π cos^2 x d x=k ∫_0^π / 2 cos^2 x d x, then the value of k is2023
• If d/(d x)(f(x))= log x, then f(x) equals:2023
• ∫ 2^x+2 dx is equal to:2023
• ∫_0^((π)/6) sec^2(x-(π)/6) dx is equal to:2023
• ∫ (2 cos 2 x-1)/(1+2 sin x) dx is equal to:2023
• ∫ e^5 log x dx is equal to:2023
• If ∫_0^a 3 x^2 dx=8, then the value of ' a ' is:2023
• ∫_0^4(e^2 x+x) dx is equal to:2023
• ∫ (sec x)/(sec x- tan x) d x equals2023
• The value of ∫_0^((π)/4)( sin 2 x) d x is2023
• ∫_-1^1 (|x-2|)/(x-2) d x, x ≠ 2 is equal to2023
• Anti-derivative of (tan x-1)/(tan x+1) with respect to x is2023
• The primitive of 2/(1+ cos 2 x) is2023
• The value of ∫_0^π / 2 log tan x dx is:2023
• Assertion: ∫_2^8 (√(10-x))/(√x+√(10-x)) d x=3 Reason (R): ∫_a^b f(x) d x=∫_a^b f(a+b-x) d x2023
• Evaluate ∫ 1/((e^x+e^-x)(e^x-e^-x)) d x log √22023
• Evaluate: ∫_0^((π)/2)[ log ( sin x)- log (2 cos x)] d x2023
• Find: ∫ 2/((1-x)(1+x^2)) d x2023
• Find: ∫ (e^x)/(√(e^2 x-4 e^x-5)) d x2023
• Evaluate ∫_0^π / 4 log (1+ tan x) d x. OR Find ∫ (d x)/(√(sin^3 x cos (x-α))).2023
• Find: ∫ (x^2+x+1)/((x+1)^2(x+2)) d x2023
• Find: ∫ (x^2)/(x^2+6 x+12) d x2023
• Find: ∫ 1/(√x(√x+1)(√x+2)) d x2023
• Evaluate: ∫_π / 4^π / 2 e^2 x((1- sin 2 x)/(1- cos 2 x)) d x OR Evaluate: ∫_-2^2 (x^2)/(1+5^x) d x2023
• Evaluate: ∫_1 / 3^1 ((x-x^3)^1 / 3)/(x^4) d x OR Evaluate: ∫_1^3{|(x-1)|+|(x-2)|} dx2023
• Find ∫ (x+2)/(√(x^2-4 x-5)) d x. OR Evaluate ∫_-a^a f(x) d x, where f(x)=(9^x)/(1+9^x).2023
• Evaluate: ∫_1^3 (√(4-x))/(√x+√(4-x)) d x2023
• Find ∫ e^cot^-1 x((1-x+x^2)/(1+x^2)) d x. log √32023
• Find: ∫ (x^2)/((x^2+4)(x^2+9)) d x2023
• Evaluate: ∫_-(π)/4^((π)/4) (cos 2 x)/(1+ cos 2 x) d x OR Find: ∫ e^x^2(x^5+2 x^3) d x2023
• Evaluate: ∫_1^e 1/(√(4 x^2-(x log x)^2)) d x2023
• Evaluate: ∫_0^π / 4 log (1+ tan x) d x2023
• Evaluate: ∫_0^2 π 1/(1+e^sin x) d x OR Find: ∫ (x^4)/((x-1)(x^2+1)) d x2023
• Find: ∫ (cos x)/(sin 3 x) d x; OR Find: ∫ x^2 log (x^2+1) d x2023
• Evaluate ∫_-1^1|x^4-x| d x. OR Find ∫ (sin^-1 x)/((1-x^2)^3 / 2) d x.2023
• Find: ∫ (e^x)/(√(5-4 e^x-e^2 x)) dx OR Evaluate: ∫_0^π / 2 √(sin x) cos^5 x d x2023
• Evaluate: ∫_0^((π)/2)| sin x- cos x| d x2023
• Find: ∫_1^4 1/(√(2 x+1)-√(2 x-1)) d x2023
• Evaluate: ∫_0^((π)/2) e^x sin x d x OR Find: ∫ 1/(cos (x-a) cos (x-b)) d x2023
• Find ∫ e^x((1- sin x)/(1- cos x)) d x2023
• Evaluate: ∫_-π / 2^π / 2 (sin^100 x)/(sin^100 x+ cos^100 x) d x2023
• Evaluate: ∫_0^((π)/2) sin 2 x tan^-1( sin x) d x2023
• Find: ∫ dx/(√(4 x-x^2))2022
• Find: ∫ dx/(x^2 - 6x + 13)2022
• If d/(d x)[ F(x)]=(sec^4 x)/(cosec^4 x) and F((π)/4)=(π)/4, then find F(x). OR Find: ∫ (log x-3)/(( log x)^4) d x.2022
• Find: ∫ (sin 3 x)/(sin x) d x OR Evaluate: ∫_0^1/2 log 3 (e^x)/(e^2 x+1) dx2022
• Find: ∫ (√(cot x))/(sin x cos x) d x OR Find: ∫ 1/(x(x^2+4)) d x2022
• Evaluate: ∫_0^1 x^2 e^x d x2022
• Evaluate: ∫_0^2 π (d x)/(1+e^sin x)2022
• Evaluate: ∫_0^π / 4 (d x)/(1+ tan x)2022
• Evaluate: ∫_0^1 tan^-1 x d x OR Find: ∫ (2 x)/(x^2+3 x+2) d x2022
• Evaluate: ∫_-1^2|x^3-x| d x2022
• Find: ∫ 1/(e^x+1) dx OR Evaluate: ∫_1^4{|x|+|3-x|} d x2022
• Evaluate: ∫_1^3 (√x)/(√x+√(4-x)) dx2022
• Find: ∫ (x^3+x)/(x^4-9) d x. OR Evaluate, using properties: ∫_-π^π(3 sin x-2)^2 d x2022
• Find: ∫ (d x)/(√x+√[3]x). OR Evaluate: ∫_0^π / 2 (cos x)/((1+ sin x)(4+ sin x)) d x.2022
• Find: ∫ e^x · sin 2 x d x OR Find: ∫ (2 x)/((x^2+1)(x^2+2)) d x2022
• Evaluate: ∫_((-π)/2)^((π)/2)( sin |x|+ cos |x|) d x2022
• Evaluate: ∫_0^π / 2 1/(1+( tan x)^2 / 3) d x2022
• Evaluate: ∫_-3^3 (x^4)/(1+e^x) d x2022
• Find: ∫ (x^2)/((x^2+1)(3 x^2+4)) d x OR Evaluate: ∫_-2^1 √(5-4 x-x^2) d x2022
• Evaluate: ∫_0^π x/(9 sin^2 x+16 cos^2 x) d x2022
• Evaluate: ∫_0^1 x(1-x)^n d x2022
• Evaluate: ∫_0^π / 2 x/(sin x+ cos x) d x Case-Study Based Question2022
• Evaluate: ∫_0^π x/(1+ sin x) d x2022asked 2×
• Evaluate: ∫_0^π / 2(2 log cos x- log sin 2 x) d x Case-Study Based Question2022

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