# Evaluate the following integrals or state that they diverge. \int_{-2}^{2}\frac{dp}{4-p^{2}}

Evaluate the following integrals or state that they diverge.
${\int }_{-2}^{2}\frac{dp}{4-{p}^{2}}$
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Step 1
Consider the provided improper integral,
${\int }_{-2}^{2}\frac{dp}{4-{p}^{2}}$
Evaluate the following integrals.
Apply the substitution method,
Let .
$p=-2⇒u=\frac{\pi }{2}$
$p=2⇒u=-\frac{\pi }{2}$
Step 2
So, the integral becomes.
${\int }_{-2}^{2}\frac{dp}{4-{p}^{2}}={\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}1du$
$={\left[1\cdot u\right]}_{-\frac{\pi }{2}}^{\frac{\pi }{2}}1du$
$={\left[u\right]}_{-\frac{\pi }{2}}^{\frac{\pi }{2}}$
$=\frac{\pi }{2}+\frac{\pi }{2}$
$=\pi$
Hence.