Integrals

CBSE Class 12 Mathematics · every board question from this chapter, 2022–2026 · 59 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 is2026asked 3×
• ∫ (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 is2026asked 3×
• ∫ dx√25-16 x^2 is equal to:2026asked 3×
• ∫ 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 dxe^x+e^-x= tan^-1 e+k, then the value of k is:2026asked 3×
• ∫ dx2^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:2026asked 3×
• 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 x2026asked 3×
• 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 x2026asked 3×
• Evaluate: ∫ (π)/12^(5 π)/12 ( d x)/(1+√ cot x) OR Evaluate: ∫ (-π)/6^(π)/2( sin x + cos x ) d x2026asked 3×
• Find: ∫ (x- sin x)/(1- cos x) d x OR Evaluate: ∫ 0^2 1√x^2+2 x+3 d x2026asked 3×
• 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=0.2026asked 3×
• If /(d x)( F(x))=1/(e^x+1), then find F(x) given that F(0)= log 1/2.2026asked 3×
• Find: ∫ ( cos x)/((2+ sin x)(4+ sin x)) d x OR Find: ∫ (x+3)/(x^2+4 x+5) d x2026asked 3×
• 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 x2^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 x2026asked 3×
• 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 ≤ /2+6, then2025
• If ∫ (2^1/x)/(x^2) d x=k · 2^1/x+C, then k is equal to2025asked 3×
• ∫ √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 xe^6 log x-e^5 log x dx is equal to:2025asked 3×
• 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^-x16+9 e^-2 x dx is equal to:2025
• ∫ ( cos 2 x- cos 2 α)/( cos x- cos α) d x is equal to:2025asked 2×
• ∫ 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:2025asked 3×
• ∫ (x+5)/((x+6)^2) e^x dx is equal to:2025asked 3×
• 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: ∫ √x1+√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 x2025asked 3×
• 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= /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 x2025asked 3×
• 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).2024asked 3×
• Find: gathered ∫ x √1+2 x dx OR gathered Evaluate: ∫ 0^(π)/4^2 sin √x√x d x2024asked 3×
• Find: ∫ (e^4 x-1)/(e^4 x+1) d x2024asked 2×
• Find: ∫ cos^3 x e^ log sin x d x OR Find: ∫ 1/(5+4 x-x^2) d x2024asked 3×
• 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 x2024asked 3×
• Find: ∫ x^2 log (x^2-1) d x2024
• Evaluate: gathered ∫ -2^2 √2-x/(2+x) dx OR gathered Find: ∫ 1/(x[( log x)^2-3 log x-4]) d x2024asked 3×
• Find: ∫ (2 x+3)/(x^2(x+3)) d x2024
• Evaluate: ∫ 0^π e^ cos xe^ cos x+e^- cos x d x OR Find: ∫ (2 x+1)/((x+1)^2(x-1)) d x2024asked 3×
• Find: ∫ (x^2)/((x^2+4)(x^2+9)) d x OR Evaluate: ∫ 1^3( x-1 + x-2 + x-3 ) dx2024asked 3×
• 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 x2024asked 3×
• Find: ∫ (√x)/((x+1)(x-1)) d x2024
• Find: ∫ x^2 · sin^-1(x^3 / 2) d x2024asked 2×
• 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: gathered ∫ 0^(π)/4 ( sin x+ cos x)/(9+16 sin 2 x) dx OR gathered 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:2023asked 3×
• ∫ 0^(π)/6 sec^2(x-(π)/6) dx is equal to:2023asked 3×
• ∫ (2 cos 2 x-1)/(1+2 sin x) dx is equal to:2023
• ∫ e^5 log x dx is equal to:2023asked 3×
• If ∫ 0^a 3 x^2 dx=8, then the value of ' a ' is:2023asked 2×
• ∫ 0^4(e^2 x+x) dx is equal to:2023
• ∫ ( sec x)/( sec x- tan x) d x equals2023asked 3×
• The value of ∫ 0^(π)/4( sin 2 x) d x is2023
• ∫ -1^1 ( x-2 )/x-2 d x, x ≠ 2 is equal to2023asked 2×
• Anti-derivative of ( tan x-1)/( tan x+1) with respect to x is2023asked 2×
• 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 x2023asked 3×
• Evaluate ∫ 1/((e^x+e^-x)(e^x-e^-x)) d x log √22023asked 3×
• Evaluate: ∫ 0^(π)/2[ log ( sin x)- log (2 cos x)] d x2023asked 2×
• 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 x2023asked 2×
• Evaluate: ∫ π / 4^π / 2 e^2 x((1- sin 2 x)/(1- cos 2 x)) d x OR Evaluate: ∫ -2^2 x^21+5^x d x2023asked 3×
• 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^x1+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 √32023asked 2×
• 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 11+e^ sin x d x OR Find: ∫ (x^4)/((x-1)(x^2+1)) d x2023asked 2×
• Find: Find: ∫ x^2 log (x^2+1) d x2023asked 3×
• 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 x2023asked 2×
• 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 x2023asked 3×
• 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 x2023asked 2×
• Find: ∫ dx√4 x-x^22022asked 3×
• Find: ∫ dx/(x^2 - 6x + 13)2022asked 3×
• If /(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.2022asked 3×
• Find: ∫ ( sin 3 x)/( sin x) d x OR Evaluate: ∫ 0^1/2 log 3 e^xe^2 x+1 dx2022asked 2×
• 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 x2022asked 3×
• 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 x2022asked 3×
• Evaluate: ∫ -1^2 x^3-x d x2022
• Find: ∫ 1e^x+1 dx OR Evaluate: ∫ 1^4 x + 3-x d x2022asked 3×
• 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.2022asked 2×
• Find: ∫ e^x · sin 2 x d x OR Find: ∫ (2 x)/((x^2+1)(x^2+2)) d x2022asked 3×
• 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 x2022asked 3×
• Evaluate: ∫ 0^π x/(9 sin^2 x+16 cos^2 x) d x2022
• Evaluate: ∫ 0^1 x(1-x)^n d x2022asked 2×
• Evaluate: ∫ 0^π / 2 x/( sin x+ cos x) d x Case-Study Based Question2022
• Evaluate: ∫ 0^π x/(1+ sin x) d x2022
• Evaluate: ∫ 0^π / 2(2 log cos x- log sin 2 x) d x Case-Study Based Question2022

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