Integration (original) (raw)

Given i=√-1, what will be the evaluation of the integral [Tex]\int_{0}^{\pi/2} \frac{\cos x + i\sin x}{\cos x - i\sin x} dx[/Tex]?

[Tex]\int_{0}^{\pi/4} \frac{1 - \tan x}{1 + \tan x} dx[/Tex] is equivalent to

If [Tex]\int_{0}^{2\pi} |x \sin x| dx = k \pi,[/Tex] then the value of k is equal to _____.

The value of the integral given below is:

[Tex]\int_{0}^{\pi} x^2 \cos x dx[/Tex]

If for non-zero x,

a f(x) + bf(1/x) = 1/x - 25 where (a ≠ b ), then [Tex]\int_{1}^{2} f(x) ~dx[/Tex] is:

• [Tex]\frac{1}{a^2 - b^2} \left[ a(\ln 2 - 25) + \frac{47b}{2} \right][/Tex]
• [Tex]\frac{1}{a^2 - b^2} \left[ a(2 \ln 2 - 25) - \frac{47b}{2} \right][/Tex]
• [Tex]\frac{1}{a^2 - b^2} \left[ a(2 \ln 2 - 25) + \frac{47b}{2} \right][/Tex]
• [Tex]\frac{1}{a^2 - b^2} \left[ a(\ln 2 - 25) - \frac{47b}{2} \right][/Tex]

Find the Integral value of f(x) = x × sin x within the limits 0, and π.

What is the value of

The value of the definite integral

is _______. (Rounded off to the nearest integer)

Evaluate the integral

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