Advertisements
Advertisements
Question
Evaluate the following using properties of definite integral:
`int_(-1)^1 log ((2 - x)/(2 + x)) "d"x`
Sum
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
Definite Integrals
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
\[\int\limits_0^{\pi/4} x^2 \sin\ x\ dx\]
\[\int\limits_{\pi/2}^\pi e^x \left( \frac{1 - \sin x}{1 - \cos x} \right) dx\]
\[\int\limits_0^{2\pi} e^{x/2} \sin\left( \frac{x}{2} + \frac{\pi}{4} \right) dx\]
\[\int\limits_0^{\pi/2} \sin^3 x\ dx\]
\[\int\limits_{- 1}^1 5 x^4 \sqrt{x^5 + 1} dx\]
\[\int\limits_0^{\pi/4} \tan^2 x\ dx .\]
If f (a + b − x) = f (x), then \[\int\limits_a^b\] x f (x) dx is equal to
Evaluate the following using properties of definite integral:
`int_0^1 log (1/x - 1) "d"x`
Evaluate the following:
`int_0^oo "e"^(-4x) x^4 "d"x`
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
