Question
Download Solution PDFWhat is \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\) equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept Used:
- \(\rm \int cos x \space dx = sin x \)
- \(e^{ln(f(x))} = f(x)\)
Calculation:
Let I = \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\)
According to the concept used
⇒ 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
∴ The value of the integral \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\) is 1.
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