Q. $\int_{}^{}{\left( \sin x - \cos x \right)^{4}\left( \sin x + \cos x \right)dx}$ is equal to
A) $\frac{\sin x - \cos x}{5} + c$
B) $\frac{\left( \sin x - \cos x \right)^{5}}{5} + c$
C) $\frac{\left( \sin x - \cos x \right)^{4}}{4} + c$
D) $\frac{\left( \sin x + \cos x \right)^{5}}{5} + c$
Explanation
(b)
Let $I = \int_{}^{}{\left( \sin x - \cos x \right)^{4}\left( \sin x + \cos x \right)dx}$
Put $\sin x - \cos x = t \Rightarrow \left( \cos x + \sin x \right)dx = dt$
$\therefore\ I = \int_{}^{}t^{4}\ dt = \frac{t^{5}}{5} + c = \frac{\left( \sin x - \cos x \right)^{5}}{5} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.