The integral integral sin^2 8x dx is equal to a. fraction x 2 - fraction sin 16x 32 + C b....

Question:

The integral {eq}\displaystyle \int \sin^2 (8x) \ dx {/eq} is equal to

{eq}\text{a.} \ \dfrac{x}{2} - \dfrac{ \sin(16x)}{32} + \text{C} \\ \text{b.} \ \dfrac{x}{2} - \dfrac{ \sin(16x)}{16} + \text{C} \\ \text{c.} \ \dfrac{x}{2}+ \dfrac{ \sin(16x)}{16} + \text{C} \\ \text{d.} \ \dfrac{x}{2}+ \dfrac{ \sin(16x)}{32} + \text{C} {/eq}

Integration:

To find the area under any curve, integration is used to find the area under that curve.

Use the following formula:

{eq}\sin^2\theta=\frac{1-\cos2\theta}{2} {/eq}

Answer and Explanation: 1

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Let {eq}I=\displaystyle \int \sin^2 (8x) \ dx {/eq}.

Use the formula {eq}\sin^2\theta=\frac{1-\cos2\theta}{2} {/eq}.

Put {eq}\theta=8x {/eq}.

So...

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Integration Problems in Calculus: Solutions & Examples

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Chapter 13 / Lesson 13
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Learn what integration problems are. Discover how to find integration sums and how to solve integral calculus problems using calculus example problems.


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