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Chapter 8: Problem 7

Find the indefinite integral. $$ \int \sin 2 x d x $$

Short Answer

Expert verified
The indefinite integral of \(\sin 2x\), \(\int \sin 2x dx\), is \(-\frac{1}{2} \cos 2x + C\).

Step by step solution

01

Identify the inner function

The function inside the sine function is \(2x\), so we'll use the chain rule for integration. We know that the integral of \(\sin u du\) is \(-\cos u + C\). Here, \(u = 2x\).
02

Apply Chain Rule

We can rewrite the integral as \(\frac{1}{2}\int \sin u du\), using \(u = 2x\). Now, the integral becomes \(-\frac{1}{2} \cos u + C\).
03

Substitute back

Now we substitute \(u = 2x\) back into the equation to get the answer. So, the indefinite integral becomes \(-\frac{1}{2} \cos 2x + C\).

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