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Problem 57 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^{\pi/6}_0 \frac{\sin t}{\cos^ 2 t} \, dt $

Answer

$\frac{2}{\sqrt{3}}-1$

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Video Transcript

for this question. We know that we can substitute coastline Tease you. Therefore, we end up with negative sign T g t is Do you therefore negative D'You is signed T d t. And the upper limits of integration is coast on power six, which using your unit circle a squirt of three over two. And then we have Cosenza on the bottom, which is simply one. Take the integral using the power rule which means increased the expert by one divide by the new exponents which gives us one over. You pull again using the fundamental form of calculus. Subtract and we end up with two over squared of three minus one.