Question on: JAMB Mathematics - 2011
Find \(\int^{1}_{0}\) 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
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Correct Option: D
\(\int^{1}_{0}\) cos4 x dx
let u = 4x
\(\frac{dy}{dx}\) = 4
dx = \(\frac{dy}{4}\)
\(\int^{1}_{0}\)cos u. \(\frac{dy}{4}\) = \(\frac{1}{4}\)\(\int\)cos u du
= \(\frac{1}{4}\) sin u + k
= \(\frac{1}{4}\) sin4x + k
let u = 4x
\(\frac{dy}{dx}\) = 4
dx = \(\frac{dy}{4}\)
\(\int^{1}_{0}\)cos u. \(\frac{dy}{4}\) = \(\frac{1}{4}\)\(\int\)cos u du
= \(\frac{1}{4}\) sin u + k
= \(\frac{1}{4}\) sin4x + k
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