Evaluate the integral: {eq}\int_{0}^{\frac{\pi }{2}} \frac{-4 \cos t}{ \sqrt{1 + \sin^2 t} } \, \mathrm{d}t {/eq}.

Question:

Evaluate the integral: {eq}\int_{0}^{\frac{\pi }{2}} \frac{-4 \cos t}{ \sqrt{1 + \sin^2 t} } \, \mathrm{d}t {/eq}.

Definite Integral:

To evaluate a definite integral of a function {eq}f(x) {/eq} over an interval {eq}[a, b] {/eq}, we follow these two steps:

1) Evalutate the indefinite integral of the function

2) Use the given boundary limits to find the value of the definite integral

Answer and Explanation: 1

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We are given to evaluate

{eq}\int_{0}^{\frac{\pi }{2}} \frac{-4 \cos t}{ \sqrt{1 + \sin^2 t} } \, \mathrm{d}t {/eq}

Step 1: First we evaluate the...

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Definite Integrals: Definition

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Chapter 12 / Lesson 6
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A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.


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