Integrals

JEE Main 2024 (Online) 5th April Morning ShiftMCQMedium📈 Topic in 24% papers+4−1

Ques. 1JEE Main 2024, 5 April (Morning Shift)

The integral 0 /4 136 x3 x + 5 x dx is equal to :

Answer

(1) 3 - 50 e 2 + 20 e 5

Numerator = A(Denominator) + B(derivative of Denominator):

136 x = A(3 x + 5 x) + B(3 x - 5 x)

3A - 5B = 136, 5A + 3B = 0 A = 12, B = -20

I = [12x - 20 e(3 x + 5 x) ]0 /4

= 3 - 20 [ e 8 2 - e 5 ] = 3 - 20 e 25/2 + 20 e 5

= 3 - 50 e 2 + 20 e 5

Answer: (1)

Ques. 2JEE Main 2024, 5 April (Morning Shift)

The value of - 2y(1 + y)1 + 2 y dy is :

Ques. 3JEE Main 2024, 5 April (Evening Shift)

Let (m, n) = 01 xm - 1(1 - x)n - 1 dx, m, n > 0. If 01 (1 - x10 )20 dx = a (b, c), then 100(a + b + c) equals .

Ques. 4JEE Main 2024, 5 April (Evening Shift)

If f(t) = 0 2x dx1 - 2 t 2 x, 0 < t < , then the value of 0 2 2 dtf(t) equals .

Ques. 5JEE Main 2024, 4 April (Morning Shift)

Let f(x)= cases-2, & -2 x 0 \ x-2, & 0<x 2 cases and h(x)=f(|x|)+|f(x)|. Then -22 h(x) dx is equal to:

Ques. 6JEE Main 2024, 4 April (Morning Shift)

If 0 4 2x1+ x x dx= 1a e ( a3 )+ b 3, where a, b , then a+b is equal to .

Ques. 7JEE Main 2024, 4 April (Evening Shift)

If the value of the integral -11 x1 + 3x dx is 2 , then a value of is

Ques. 8JEE Main 2024, 4 April (Evening Shift)

If 5 x dx = x cosec x (cosec2 x + 32 ) + e | x2 | + C where , R and C is the constant of integration, then the value of 8( + ) equals .

Ques. 9JEE Main 2024, 1 February (Morning Shift)

The value of the integral 0 /4 x dx 4(2x)+ 4(2x) equals :

Ques. 10JEE Main 2024, 1 February (Morning Shift)

If - /2 /2 8 2 x dx (1+e x ) (1+ 4x )= + e(3+2 2), where , are integers, then 2+ 2 equals :

Ques. 11JEE Main 2024, 1 February (Evening Shift)

If 0 /3 4 x d x=a +b 3, where a and b are rational numbers, then 9 a+8 b is equal to :

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