MHT CET · Maths · Definite Integration
\(\int_{-5}^{5} \log \left(\frac{7-x}{7+x}\right) d x=\)
- A 5
- B 0
- C -5
- D 10
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
(B)
Let \(1=\int_{-4}^{5} \log \frac{7-x}{7+x}\)
Let \(\quad f(x)=\log \frac{7-x}{7+x}\)
\(f(-x)=\log \left[\frac{7-(-x)}{7+(-x)}\right]=\log \left(\frac{7+x}{7-x}\right)=-\log \left(\frac{7-x}{7+x}\right)=\) \(-f(x)\)
\(\therefore f(x)\) is an odd function \(\Rightarrow I=0\)
Let \(1=\int_{-4}^{5} \log \frac{7-x}{7+x}\)
Let \(\quad f(x)=\log \frac{7-x}{7+x}\)
\(f(-x)=\log \left[\frac{7-(-x)}{7+(-x)}\right]=\log \left(\frac{7+x}{7-x}\right)=-\log \left(\frac{7-x}{7+x}\right)=\) \(-f(x)\)
\(\therefore f(x)\) is an odd function \(\Rightarrow I=0\)
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