Mathematics

$\int$ sin x d(cos x) is equal to

$-\dfrac{1}{4}cos2x+c$

SOLUTION

Consider the given equation:

$:\int{\sin x\,d}(\cos x)dx$

$=\int{\sin (x)\cos (x)dx}$

$=\int{\dfrac{\sin (2x)}{2}}dx$

$=\dfrac{1}{2}\int{\sin (2x)dx}$

$\,\,\,\text{put}\,\text{then}\,\,v=2x$

$\,\,\,\text{so}\,\text{that}\,\,dv=2dx$

$=\dfrac{1}{4}\int{\sin (v).(2)dx}$

$=\dfrac{1}{4}\int{\sin (v)dx}$

$=-\dfrac{1}{4}\cos (v)+c$

$=-\dfrac{1}{4}\cos (2x)+c$

$Hence\,,this\,\,is\,\,the\,\,answer.$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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