Question
Download Solution PDF\(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त अवधारणा:
- \(\rm \int cos x \space dx = sin x \)
- \(e^{ln(f(x))} = f(x)\)
गणन:
मान लीजिए I = \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\)
प्रयुक्त अवधारणा के अनुसार
⇒ I = \(\rm \int^\frac{\pi}{2}_0 (cos x) dx\)
⇒ \(\rm [sinx]_{0}^{\frac{\pi }{2}}\)
⇒ \(\rm sin \frac{\pi }{2} - sin 0\)
⇒ 1 - 0 = 1
∴ समाकल \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\) का मान 1 है।
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