Use symmetry to evaluate the following integral. $$ \int_{-\pi/6}^{\pi/6} 4 \sec^2 x \, dx $$ $$ \int_{-\pi/6}^{\pi/6} 4 \sec^2 x \, dx = \boxed{} $$
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Step 1: Observe that the integrand f(x)=4 sec^2 x is even because sec^2(-x)=sec^2 x, so f(-x)=f(x). Show more…
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