Definite Integration Questions

Let (the set of all real numbers) be a positive, non-constant and differentiable function such that f′(x) Then the value of lies in the interval...

The value of is

Let f be a non-negative function defined on the interval [0, 1]. If f(t)dt, 0 ≤ x ≤ 1, and f(0) = 0, then...

If dx = k log then k is -...

equals -

The value of the definite integral (ex+1 + e3-x)-1 dx is

The value of the definite integral ((x + 1)ex ln x) dx is -

Let a, b, c be non-zero real numbers such that ; (1 + cos8x)(ax2 + bx + c) dx = (1 + cos8x)(ax2 + bx + c) dx, then the quadratic equation ax2 + bx + c = 0 has -...

If f(x) = A sin + B, f′ = √2 and f(x) dx = , then the constant A and B are -...

If In =tann xdx then n (In + In-2) =...

dx

Suppose , f, f′ and f″ are continuous on [0, e] and that f′(e) = f(e) = f(1) = 1 and dx = , then the value of f″(x) ln x dx equals -...

dx has the value equal to -

dx =

Suppose that F(x) is an anti derivative of f(x) = , x > 0 then dx can be expressed as -...

dx

Integral|sin 2πx| dx is equal to -

dx =

dx is equal to -

(cos ax - sin bx)2 dx where a and b are integer is equal to -