MHT CET · Maths · Definite Integration
\(\int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{\mathrm{e}^{\mathrm{x}}-1}{\mathrm{e}^{\mathrm{x}}+1}\right) \mathrm{dx}=\)
- A \(2 \log 2\)
- B \(-2 \log 2\)
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\(\int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{\mathrm{e}^{\mathrm{x}}-1}{\mathrm{e}^{\mathrm{x}}+1}\right) \mathrm{dx}=\int_{-\log 2}^{\log 2} \sin \left(\frac{\mathrm{e}^{\mathrm{x}}-1}{\mathrm{e}^{\mathrm{x}}+1}\right)\) \(\mathrm{dx}=0\)
\({\left[\because \sin \left(\frac{\mathrm{e}^{\mathrm{x}}-1}{\mathrm{e}^{\mathrm{x}}+1}\right) \text { is an odd function }\right]}\)
\({\left[\because \sin \left(\frac{\mathrm{e}^{\mathrm{x}}-1}{\mathrm{e}^{\mathrm{x}}+1}\right) \text { is an odd function }\right]}\)
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