Mathematics

Solve:$$\int _{ 0 }^{ \log { 2 }  }{ \cos { 2x } dx } $$=


SOLUTION
$$\displaystyle\int_{0}^{\log{2}}{\cos{2x}dx}$$

Let $$t=\sin{2x}\Rightarrow dt=2\cos{2x}dx\Rightarrow \cos{2x}dx=\dfrac{dt}{2}$$

When $$x=0\Rightarrow t=0$$

When $$x=\log{2}\Rightarrow t=\sin{2\log{2}}$$

$$=\displaystyle\int_{0}^{\sin{2\log{2}}}{\dfrac{dt}{2}}$$

$$=\dfrac{1}{2}\left[t\right]_{0}^{\sin{2\log{2}}}$$

$$=\dfrac{1}{2}\left[\sin{2\log{2}}-0\right]$$

$$=\dfrac{1}{2}\sin{2\log{2}}$$
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Subjective Medium Published on 17th 09, 2020
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