Newton-Leibnitz Formula

JEE Main Mathematics · Definite Integration · 16 questions, latest first

• 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 integral ∫_0^1 cot^-1(1+x+x^2) d x is equal to:20264 April, Shift 2 · Q20
• Let f be a polynomial function such that f(x^2+1)=x^4+5 x^2+2, for all x ∈ R. Then ∫_0^3 f(x) d x is equal to202628 January, Shift 1 · Q16
• If f(x) satisfies the relation f(x)=e^x+∫_0^1(y+x e^x) f(y) d y, then e+f(0) is equal to ____.202624 January, Shift 2 · Q25
• The number of elements in the set S={x: x ∈[0,100] and ∫_0^x t^2 sin (x-t) d t=x^2} is ____202623 January, Shift 2 · Q24
• 4 ∫_0^1(1/(√(3+x^2)+√(1+x^2))) d x-3 log_e(√3) is equal to:20252 April, Shift 2 · Q18
• The integral ∫_0^π / 4 (136 sin x)/(3 sin x+5 cos x) d x is equal to:20245 April, Shift 1 · Q11
• If ∫_0^((π)/3) cos^4 x d x=a π+b √3, where a and b are rational numbers, then 9 a+8 b is equal to:20241 February, Shift 2 · Q10
• Let f: R → R be defined as f(x)=a e^2 x+b e^x+c x. If f(0)=-1, f^′( log_e 2)=21 and ∫_0^log_e 4(f(x)-c x) d x=39/2, then the…202430 January, Shift 2 · Q10
• If ∫_0^1 1/(√(3+x)+√(1+x)) d x=a+b √2+c √3, where a, b, c are rational numbers, then 2 a+3 b-4 c is equal to:202427 January, Shift 1 · Q11
• Let for x ∈ R, S_0(x)=x, S_k(x)=C_k x+k ∫_0^x S_k-1(t) d t, where C_0=1, C_k=1-∫_0^1 S_k-1(x) d x, k=1,2,3, …. Then S_2(3)+6 C_3…202313 April, Shift 1 · Q25
• Let α>0. If ∫_0^α x/(√(x+α)-√x) d x=(16+20 √2)/15, then α is equal to:202331 January, Shift 2 · Q70
• Let α ∈(0,1) and β= log_e(1-α). Let P_n(x)=x+x^2/2+x^3/3+…+x^n/n, x ∈(0,1). Then the integral ∫_0^α (t^50)/(1-t) d t is equal to202331 January, Shift 1 · Q70
• Let f(x)=x+a/(π^2-4) sin x+b/(π^2-4) cos x, x ∈ R be a function which satisfies f(x)=x+∫_0^π / 2 sin (x+y) f(y) d y. Then (a+b)…202329 January, Shift 1 · Q68
• ∫_((3 √2)/4)^((3 √3)/4) 48/(√(9-4 x^2)) d x is equal to202324 January, Shift 2 · Q72