Wednesday, July 21, 2021

Integral of sin 2 x | What is the sin(x)^2 integral?

In this math lesson, we will tell you what the integral of sin x 2 is. So what is the integral of sin(x)^2? What is the integral of sin(x) to the 2nd? You can see the proof and solution in our article. We wish you good integral solving in advance.

$sin^2x$ Integral | Integral of Sin2(x)

For the integral of sinx to the 2nd, we first need to write the expansion of sin^2(x).

$sin^2x$ expansion(transform-conversion):

  • $sin^2x=\frac{1-cos2x}{2}$

Now let's move on to the step-by-step solution:

→ $sin^2x=\frac{1-cos2x}{2}=\frac{1}{2}-\frac{cos2x}{2}$

→ $\int{(\frac{1}{2}-\frac{cos2x}{2})dx}$

→ $\int{\frac{1}{2}dx}-\int{\frac{cos2x}{2}dx}$

→ $\frac{x}{2}-\frac{sin2x}{4}$

As a result, our answer is $\frac{x}{2}-\frac{sin2x}{4}$. (Answer = x/2 - sin2x/4)

Answer > $sin^2x$ integral = $\frac{x}{2}-\frac{sin2x}{4}$


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