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Evaluate the integral.

{eq}\displaystyle \int_0^{\frac{\pi}{2}} \frac{\cos t}{\sqrt {1+ \sin^2 t}}\ dt {/eq}.

Question:

Evaluate the integral.

{eq}\displaystyle \int_0^{\frac{\pi}{2}} \frac{\cos t}{\sqrt {1+ \sin^2 t}}\ dt {/eq}.

Evaluating the Integral:

The objective is to evaluate the given integral.

The given integral function is {eq}\int_{0}^{\frac{\pi}{2}} \left (\frac{\cos t}{\sqrt{1 + \sin^{2} t}} \right ) dt {/eq}

First, we have to differentiate with respect to {eq}t. {/eq}

Then, we have to integrate the function and get a solution.

Answer and Explanation: 1

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The given integral {eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \left (\frac{\cos t}{\sqrt{1 + \sin^{2} t}} \right ) dt {/eq}

Differentiate the...

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Work as an Integral

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Chapter 7 / Lesson 9
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Learn the work done formula and understand the application of work integral in the work done formula with examples problems using calculus.


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