# My mathematical physics test

Calculus Level 4

Let $$k$$ be a real number. Evaluate the integral

$\frac{1}{\pi} \int_{0}^{\pi} e^{k \cos(\theta)} \cos(k \sin(\theta)) d\theta.$

• Hint: you may want to solve this one, first: Suppose C is the circumference $$|z| = 1$$. Let $$k$$ and $$a < 1$$ be real numbers and $$n$$ a natural number. Evaluate the integral

$I_{n}(z, a) = \oint_{C} \frac{e^{kz}}{(z-a)^{n}} dz.$

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