Definite Integration

JEE Main Mathematics · 14 questions

All questions, latest first

• The value of the integral ∫_0^2 (√(x(x^2+x+1)))/((√(x+1))(√(x^4+x^2+1))) d x is equal to:20268 April, Shift 2 · Q16
• Let f(x)= {1/3, x ≤ π / 2; (b(1- sin x))/((π-2 x)^2), x>π / 2}. If f is continuous at x=π / 2, then the value of ∫_0^3 b-6|x^2+2…20268 April, Shift 2 · Q19
• If ∫_π / 6^π / 4( cot (x-(π)/3) cot (x+(π)/3)+1) d x=α log_e(√3-1), then 9 α^2 is equal to ____.20268 April, Shift 2 · Q22
• Let A= [1, 3, -1; 2, 1, α; 0, 1, -1] be a singular matrix. Let f(x)=∫_0^x(t^2+2 t+3) dt, x ∈[1, α]. If M and m are respectively…20266 April, Shift 2 · Q17
• The value of the integral ∫_-1^1((x^3+|x|+1)/(x^2+2|x|+1)) d x is equal to:20266 April, Shift 2 · Q20
• The value of the integral ∫_-(π)/4^((π)/4)((32 cos^4 x)/(1+e^sin x)) d x is:20266 April, Shift 1 · Q18
• Let (2^1-a+2^1+a), f(a),(3^a+3^-a) be in A.P. and α be the minimum value of f(a). Then the value of the integral…20265 April, Shift 2 · Q18
• The value of the integral ∫_0^∞ (log_e(x))/(x^2+4) d x is:20265 April, Shift 1 · Q18
• The value of the integral ∫_((π)/6)^((π)/3)((4-cosec^2 x)/(cos^4 x)) d x is:20265 April, Shift 1 · Q20
• The integral ∫_0^1 cot^-1(1+x+x^2) d x is equal to:20264 April, Shift 2 · Q20
• Let ∫_-2^2(| sin x|+[x sin x]) d x=2(3- cos 2)+β, where [·] is the greatest integer function. Then β sin ((β)/2) equals:20264 April, Shift 1 · Q19
• The value of ∫_0^20 π( sin^4 x+ cos^4 x) d x is equal to:20262 April, Shift 2 · Q17
• Let [·] denote the greatest integer function. Then the value of ∫_0^3((e^x+e^-x)/([x]!)) d x is:20262 April, Shift 1 · Q19
• If α=∫_0^2 √3 log_2(x^2+4) d x+∫_2^4 √(2^x-4) d x, then α^2 is equal to ____.20262 April, Shift 1 · Q25