Properties of Definite Integrals: JEE Questions & Solutions

The value of - /6^ /6 +4x^111- (|x|+ /6) dx is equal to:

The number of elements in the set S = x: x [0, 100] and 0^x t^2 (x-t) dt = x^2 is

If - 2^ 2 96x^2 ^2 x1 + e^x dx = (a ^2 +), a, Z, then (a +)^2 equals:

The integral 0^ 8x dx4 ^2 x + ^2 x is equal to

The integral 0^ (x + 3) x1 + 3 ^2 x dx is equal to:

Let f(x) = 0^x g(t) ( 1 - t1 + t) dt, where g is a continuous odd function. If - /2^ /2 ( f(x) x^2 (x)1 + e^x) dx = ^24 -, then is equal to:

Let f: R R be a function defined by f(x) = 4x4x + 2 and M = f(1-a)^f(a) x ^4(x(1 - x)) dx, N = f(1-a)^f(a) ^4(x(1 - x)) dx; a 12. If M =…

The value of 0^1 (2x^3 - 3x^2 - x + 1)^1/3 dx is equal to:

The value of k N for which the integral In = 0^1 (1 - x^k)^n dx, n N, satisfies 147I20 = 148I21, is:

The value of the integral - 4^ 4 x + 42 - 2x dx is:

If 0^ 5^ x (1 + x 3x + ^2 x + ^3 x 3x)1 + 5^ x dx = k 16, then k is equal to.

Let f(x) be a function satisfying f(x) + f( - x) = ^2, for all x R. Then 0^ f(x) x dx is equal to:

For m, n 0, let (m,n) = 0^1 (1 + 3t)^n dt. If (10,6) = 0^1 (1 + 3t)^6 dt and (11,5) = p(14)^5, then p is equal to:

If f: R R is a continuous function satisfying 0^ 2 f( 2x) x dx + 0^ 4 f( 2x) x dx = 0, then the value of is:

If 0^1 1(5+2x-2x^2) (1+e^(2-4x)) dx = 1 e ( +1),, 0, then ^4- ^4 is equal to