Trigonometric Integral

Calculus Level 2

Compute the definite integral: 02πecosθcos(sinθ)dθ.\int_{0}^{2\pi} e^{\cos \theta} \cos(\sin\theta) \, d\theta.

Hint: Consider the function f(t)=02πetcosθcos(tsinθ)dθf(t) = \int_{0}^{2\pi} e^{t \cos\theta} \cos(t\sin\theta) \, d\theta

and use differentiation under the integral sign.

×

Problem Loading...

Note Loading...

Set Loading...