Q. $\int_{}^{}{({\sin^{4}x}{- \cos^{4}{x)dx}}}$ is equal to
A) $- \frac{\cos{2x}}{2} + c$
B) $- \frac{\sin{2x}}{2} + c$
C) $\frac{\sin{2x}}{2} + c$
D) $\frac{\cos{2x}}{2} + c$
Explanation
(b)
$\int_{}^{}{({\sin^{4}x}{- \cos^{4}{x)dx}}}$
$= \int_{}^{}{(\sin^{2}{x - \cos^{2}{x)(\sin^{2}{x + \cos^{2}{x)dx}}}}}$
$= \int_{}^{}{(\sin^{2}{x - \cos^{2}{x)dx = - \int_{}^{}{(\cos^{2}{x - \sin^{2}{x)dx}}}}}}$
$= - \int_{}^{}{\cos{2x\ dx = \frac{- \sin{2x}}{2} + c}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.