Evaluation by Substitution

JEE Main Mathematics · Definite Integration · 20 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 (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 ∫_((π)/6)^((π)/3)((4-cosec^2 x)/(cos^4 x)) d x is:20265 April, Shift 1 · Q20
• The integral 80 ∫_0^((π)/4)((sin θ+ cos θ)/(9+16 sin 2 θ)) d θ is equal to:202529 January, Shift 1 · Q18
• Let for f(x)=7 tan^8 x+7 tan^6 x-3 tan^4 x-3 tan^2 x, I_1=∫_0^π / 4 f(x) d x and I_2=∫_0^π / 4 x f(x) d x. Then 7 I_1+12 I_2 is…202522 January, Shift 1 · Q18
• Let ∫_α^log_e 4 (d x)/(√(e^x-1))=(π)/6. Then e^α and e^-α are the roots of the equation:20248 April, Shift 2 · Q11
• ∫_0^π / 4 (cos^2 x sin^2 x)/(( cos^3 x+ sin^3 x)^2) d x is equal to20246 April, Shift 1 · Q11
• If ∫_0^((π)/4) (sin^2 x)/(1+ sin x cos x) d x=1/a log_e(a/3)+(π)/(b √3), where a, b ∈ N, then a+b is equal to ____.20244 April, Shift 1 · Q25
• Let f, g:(0, ∞) → R be two functions defined by f(x)=∫_-x^x(|t|-t^2) e^-t^2 d t and g(x)=∫_0^x^2 t^1 / 2 e^-t d t. Then, the…202431 January, Shift 2 · Q12
• If the integral 525 ∫_0^((π)/2) sin 2 x cos^(11/2) x(1+Cos^(5/2) x)^(1/2) d x is equal to (n √2-64), then n is equal to ____202431 January, Shift 1 · Q27
• Let y=f(x) be a thrice differentiable function in (-5,5). Let the tangents to the curve y=f(x) at (1, f(1)) and (3, f(3)) make…202430 January, Shift 2 · Q12
• Let f: R → R be a function defined by f(x)=x/((1+x^4)^1 / 4), and g(x)=f(f(f(f(x)))). Then, 18 ∫_0^√(2 √5) x^2 g(x) d x is equal…202430 January, Shift 2 · Q13
• For 0<a<1, the value of the integral ∫_0^π (d x)/(1-2 a cos x+a^2) is:202427 January, Shift 2 · Q12
• Let f_n=∫_0^((π)/2)(Σ_k=1^n sin^k-1 x)(Σ_k=1^n(2 k-1) sin^k-1 x) cos x d x, n ∈ N. Then f_21-f_20 is equal to ____202313 April, Shift 2 · Q26
• The value of the integral ∫_- log_e 2^log_e 2 e^x( log_e(e^x+√(1+e^2 x))) d x is equal to202311 April, Shift 1 · Q15
• Let f(x)=x/((1+x^n)^(1/n)), x ∈ R-{-1}, n ∈ N, n>2. If f^n(x)= (fofof.... upto n times) (x), then lim_n → ∞ ∫_0^1 x^n-2(f^n(x)) d…20236 April, Shift 2 · Q26
• If ∫_0^1(x^21+x^14+x^7)(2 x^14+3 x^7+6)^1 / 7 d x=1/l(11)^m / n where l, m, n ∈ N, m and n are coprime then l+m+n is equal to…20231 February, Shift 1 · Q85
• The value of ∫_((π)/3)^((π)/2) ((2+3 sin x))/(sin x(1+ cos x)) d x is equal to202331 January, Shift 1 · Q69
• The value of the integral ∫_1^2((t^4+1)/(t^6+1)) d t is202329 January, Shift 2 · Q67
• The integral 16 ∫_1^2 (d x)/(x^3(x^2+2)^2) is equal to202325 January, Shift 2 · Q71