Question

Explain the step which has got a star.

How can it be written like that?

Thank you.

Answer 1

$\bf HELLO \: \: DEAR,$

$\bf \frac{1}{2} \int x^{0} \: dx - \frac{1}{2} \int cos2x dx$

$\bf \frac{1}{2} .\frac{x^{0 + 1}}{0 + 1} - \frac{1}{2} \frac{sin2x}{2}$

$\bf \: \therefore \boxed{put 2x = t , \\ \\ \bf \: dt/dx = 2 dx \\ \\ \bf \: dx= \frac{1}{2}dt \\ \\ \bf \int (cost ).\frac{1}{2}dt \\ \\ \bf \: = \frac{1}{2} \int cost.dt \\ \\ \bf \: = \frac{1}{2} sint \\ \\ \bf \: = \frac{1}{2} sin2x + c}$

$\bf \frac{1}{2} x - \frac{1}{2}\frac{sin2x}{2} + c$

$\bf \frac{x}{2} - \frac{1}{4}{sin2x}+ C$

$\underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$

Answer 2

Hello Mahika Ji.


Please see the attached file.



Thanks