Question

Evaluate the definite integral. 1/4 csc(2πt) cot(2πt) dt 1/12

Answer 1

Hey there, hope I can help!

$\frac{1}{4}\csc \left(2\pi t\right)\cot \left(2\pi t\right)dt\frac{1}{12}$

$\mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}\cdot \frac{d}{e}=\frac{a\:\cdot \:b\:\cdot \:d}{c\:\cdot \:e} \ \textgreater \ \frac{1\cdot \:1\cdot \:dt}{4\cdot \:12}\csc \left(2\pi t\right)\cot \left(2\pi t\right)$

$\mathrm{Apply\:rule}\:1\cdot \:a=a \ \textgreater \ \frac{dt}{4\cdot \:12}\csc \left(2\pi t\right)\cot \left(2\pi t\right)$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:12=48 \ \textgreater \ \frac{dt}{48}\csc \left(2\pi t\right)\cot \left(2\pi t\right)$

$\mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ \frac{dt\csc \left(2\pi t\right)\cot \left(2\pi t\right)}{48}$

Hope this helps!