Problem of the Week

Updated at Mar 10, 2014 11:58 AM

This week we have another calculus problem:

How would you integrate \(\cos{7x}\)?

Let's start!



\[\int \cos{7x} \, dx\]

1
Use Integration by Substitution.
Let \(u=7x\), \(du=7 \, dx\), then \(dx=\frac{1}{7} \, du\)

2
Using \(u\) and \(du\) above, rewrite \(\int \cos{7x} \, dx\).
\[\int \frac{\cos{u}}{7} \, du\]

3
Use Constant Factor Rule: \(\int cf(x) \, dx=c\int f(x) \, dx\).
\[\frac{1}{7}\int \cos{u} \, du\]

4
Use Trigonometric Integration: the integral of \(\cos{u}\) is \(\sin{u}\).
\[\frac{\sin{u}}{7}\]

5
Substitute \(u=7x\) back into the original integral.
\[\frac{\sin{7x}}{7}\]

6
Add constant.
\[\frac{\sin{7x}}{7}+C\]

Done
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