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Question
`int_(-5)^5 log ((7 - x)/(7 + x))`dx = ?
Options
5
-5
0
10
MCQ
Solution
0
Explanation:
Let I = `int_(-5)^5 log ((7 - x)/(7 + x))`dx
f(x) = `log ((7 - x)/(7 + x))`
f(- x) = `log ((7 - x)/(7 + x))`
f(- x) = `log ((7 - x)/(7 + x))^-1`
= - `log ((7 - x)/(7 + x))`
f(- x) = - f(x)
∴ f(x) is an odd function
∴ l = 0
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Fundamental Theorem of Integral Calculus
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