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What is \(\rm \int^\frac{\pi}{2}_0 e^{ln(cos x)} dx\) equal to?
1. -1
2. 0
3. 1
4. 2

1 Answer

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Correct Answer - Option 3 : 1

Concept 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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