Evaluate the definite integral _0^ 4 2xdx - Vidyadip

Question

Evaluate the definite integral $\int\limits_0^{\frac{\pi }{4}} {\sin 2xdx}$

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Answer

$\int\limits_0^{\frac{\pi }{4}} {\sin 2xdx}$ $= \left( {\frac{{ - \cos 2x}}{2}} \right)_0^{\frac{\pi }{4}}$
$= \frac{{ - \cos \frac{\pi }{2}}}{2} - \left( {\frac{{ - \cos {0^o}}}{2}} \right)$
$ = \frac{0}{2} - \left( {\frac{{ - 1}}{2}} \right)$
$= 0 + \frac{1}{2}$
$= \frac{1}{2}$

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