Find \(\int\) cos4 x dx
A
\(\frac{3}{4}\) sin 4x + k
B
-\(\frac{1}{4}\) sin 4x + k
C
-\(\frac{3}{4}\) sin 4x + k
D
\(\frac{1}{4}\) sin 4x + k
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\int\) cos4 x dx
let u = 4x
\(\frac{dy}{dx}\) = 4
dx = \(\frac{dy}{4}\)
\(\int\)cos u. \(\frac{dy}{4}\) = \(\frac{1}{4}\)\(\int\)cos u du
= \(\frac{1}{4}\) sin u + k
= \(\frac{1}{4}\) sin4x + k
Source: Myschool Past Questions Archive (Record #29501)