Question

The derivative of \( y=\int_{0}^{\ln x}\sin(e^t)\,dt \) is :

• A. \(1\)
• B. \(\dfrac{\sin x}{x}\)
• C. \(\dfrac{\cos x}{x}\)
• D. \(1-\cos e^x\)

Hint:

For integrals with variable upper limit: \[ \frac{d}{dx}\left(\int_a^{g(x)}f(t)\,dt\right) = f(g(x))\cdot g'(x) \] Always:
• substitute the upper limit into the integrand,
• then multiply by derivative of the upper limit.

Answer 1

The Correct Option is B