Advertisements
Advertisements
Question
Evaluate the following using properties of definite integral:
`int_(-1)^1 log ((2 - x)/(2 + x)) "d"x`
Sum
Advertisements
Solution
Let f(x = `log (2 - x)/(2 + x))`
f(– x) = `log ((2 - (- x))/(2 + (– x)))`
= `log ((2 + x)/(2 - x))`
= `log ((2 - x)/(2 + x))^-1`
= `- log ((2 - x)/(2 + x))`
⇒ (fx) = – f(x)
∴ f(x) is an odd function
∴ `int_(-1)^1 log ((2 - x)/(2 + x)) "d"x` = 0
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\limits_0^\pi \left( \sin^2 \frac{x}{2} - \cos^2 \frac{x}{2} \right) dx\]
\[\int_\frac{\pi}{6}^\frac{\pi}{3} \left( \tan x + \cot x \right)^2 dx\]
\[\int_0^\pi \cos x\left| \cos x \right|dx\]
Solve each of the following integral:
\[\int_2^4 \frac{x}{x^2 + 1}dx\]
\[\int\limits_0^1 2^{x - \left[ x \right]} dx\]
\[\int\limits_{- \pi/2}^{\pi/2} \sin\left| x \right| dx\] is equal to
\[\int\limits_0^\pi \sin^3 x\left( 1 + 2 \cos x \right) \left( 1 + \cos x \right)^2 dx\]
The value of `int_2^3 x/(x^2 + 1)`dx is ______.
What is the result of a definite integral?
What are definite integrals used to find over a fixed interval?
