JAMB Mathematics 2011 Paper

Question : 36

Total: 46

Find

\int

cos4 x dx

Solution:

Concept:

Use

u

-substitution to integrate a composite cosine function.

Explanation:

Let

u = 4x

Then

\frac{du}{dx} = 4

, so

dx = \frac{du}{4}

Substitute into the integral:

\int \cos(4x)\,dx = \int \cos(u)\cdot \frac{du}{4}

= \frac{1}{4}\int \cos(u)\,du

The integral of

\cos(u)

\sin(u)

So we get:

\frac{1}{4}\sin(u) + k

Now substitute back

u = 4x

\frac{1}{4}\sin(4x) + k

Answer:

\frac{1}{4}\sin(4x) + k

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