Definite Integrals: JEE Questions & Solutions

6 0^ ( 3x + 2x + x)dx is equal to:

Let [ ] denote the greatest integer function and f(x) = n 1n^3 k=1^n [ k^23^x ]. Then 12 j=1^ f(j) is equal to.

The value of the integral - 2^ 2 1[x]+4 dx, where [ ] denotes the greatest integer function, is

Let [ ] be the greatest integer function. If = 0^64 (x^1/3-[x^1/3]) dx, then 1 0^ ^2 ^6 + ^6 d is equal to.

The value of the integral 24^ 5 24 dx1 + [3] 2x is:

Let a differentiable function f satisfy 0^36 f ( tx36)dt=4 f(x). If y=f(x) is a standard parabola passing through the points (2,1) and…

The value of r=1^20 | ( 0^r x| x| dx) | is:

Let [ ] denote the greatest integer function. Then - /2^ /2 12(3+[x])3+[ x]+[ x] dx is equal to:

MATHEMATICS SECTION-A The value of e^2^e^4 1x ( e^ ( ( e x)^2 +1)^-1e^ ( ( e x)^2 +1)^-1 + e^ ( (6- e x)^2 +1)^-1) dx is:

If I = 0^ 2 ^2 32x ^2 x + ^2 x dx, then 0^ 2 x x x ^4 x + ^4 x dx equals:

Let f: R R be a twice-differentiable function such that f(2) = 1. If F(x) = x f(x) for all x R, and the integrals 0^2 x F'(x) dx = 6 and…

The integral 80 0^ 4 ( +)(9 + 16 2) d is equal to:

Let f(x) = 1^x (t^2 - 9t + 20) dt, 1 x 5. If the range of f(x) is [, ], then 4( +) equals:

Let (a, b) be the point of intersection of the curve x^2 = 2y and the straight line y = 2x - 6 in the second quadrant. Then the integral I…

The value of -1^1 (1 + |x| - x)e^x + ( |x| - x)e^-xe^x + e^-x dx is equal to

Let f(x) + 2f ( 1x) = x^2 + 5 and 2g(x) - 3g ( 12) = x, x 0. If = 1^2 f(x) dx, = 1^2 g(x) dx, then the value of 9 + is:

The integral -1^ 32 ( ^2 x ( x)) dx is equal to:

If (a,b) is the orthocenter of a triangle with vertices (1,2), (2,3), (3,1), then 36I1/I2 is equal to:

For 0 < a < 1, find the value of the integral 0^ dx1 - 2a (x) + a^2:

For x (- 2, 2), if y(x) = (x) + (x) - (1 + (2x)) ( (x) + (x)), then y ( 4) is equal to:

If /3^ /6 1 - 2x dx = + 2 + 3, where,, are rational numbers, then 3 + 4 - is equal to:

The value of n ( k=1^n n^3(n^2+k^2)(n^2+3k^2)) is:

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 angles…

Let f: R R be defined by f(x) = ae^2x + be^x + c. If f(0) = -1, f'( e 2) = 21, and e 4^0 (f(x) - cx) dx = 392, then the value of |a + b +…

If I = 0^ 2 5 ^2 x ^ 112 x (1 + ^ 52 x)^ 12 dx, then n in I = n 2 - 64 is:

Let f(x) be defined as: f(x) = x - 2, for -2 < x < 0 f(x) = 1 - 2x, for 0 x 2 Let h(x) = f(x) + f(x). Then the integral of h(x) dx is equal…

The value of 0^9 10xx+1 dx is:

The integral 3/4^1/4 (2 ^-1 ( 1-x1+x)) dx is equal to:

Evaluate the following limit: x /2 ( /2)^3^x^3 ( (2t^1/3) + (t^1/3)) dt (x - /2)^2

The value of the integral: 3 24^ 3 34 48 9 - 4x^2 dx is equal to:

The integral 16 1^2 dxx^3(x^2+2)^2 is equal to:

If 1/3^3 | (x)| dx = mn ( n^2e), where m and n are coprime natural numbers, then m^2 + n^2 - 5 is equal to.

Let f(x) = x + a ( 2 - 4) x + b ( 2 - 4) x, x R be a function which satisfies f(x) = x + 0^ /2 (x + y)f(y) dy. Then (a+b) is equal to:

Let [x] denote the greatest integer. Consider the function f(x) = x^2, 1 + [x], where [x] denotes the greatest integer x. Then the value of…

The value of the integral 1^2 t^4 + 1t^6 + 1 dt is:

The value of the integral 1/2^2 ^-1 xx dx is equal to:

If [t] denotes the greatest integer 1, then the value of 3(e-1)^2e 1^2 x^2 e^[x] + [x^3] dx is:

If (x) = 1 x x4^x ( 4 2 t - 3 (t)) dt, x 0, then ( 4) is equal to:

If 0^1 (x^21 + x^4 + x^7)(2x^14 + 3x^7 + 6)^1/7 dx = 17 (11)^m/n where l, m, n N, and m, n are coprime, then l + m + n is equal to:

Let 5f(x) + 4f ( 1x) = 1x + 3, x0. Then 18 1^2 f(x) dx is equal to:

Let [t] denote the greatest integer t. The 6^ 5 6 (8[ x] - 5[ x]) dx is equal to:

Let f be a continuous function satisfying 0^t^2 ( f(x) + x^2) dx = 43 t^3, t 0. Then f ( ^24) is equal to:

Let the function f: [0, 2] R be defined as: f(x) = cases e^ x^2, x - x, & x [0, 1), e^x - e x, & x [1, 2), cases where t denotes the…

If -0.15^0.15 | 100x^2 - 1 | dx = k3000, then k is equal to:

JEE Main 2023 Questions with Solutions Section – A

The value of 0^ 4 e^x(e^x + ^2 x) dx is:

Let f = ( k=1^ ^k x) ( k-1 ^k x) x dx N. Then f11 is equal to: