Evaluate the following integral: {eq}\int_{0}^{\frac{\pi }{2}} \frac {\cos x} {\sqrt{1 + \sin^2 x} } \, \mathrm{d}x {/eq}.
Question:
Evaluate the following integral: {eq}\int_{0}^{\frac{\pi }{2}} \frac {\cos x} {\sqrt{1 + \sin^2 x} } \, \mathrm{d}x {/eq}.
Indefinite Integral: Substitution Rule:
We simplify this integral by using a u-substitution. This gives us an irrational integral to calculate. We use a hyperbolic sine substitution to calculate this irrational integral.
Answer and Explanation: 1
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View this answerWe calculate the integral by using the substitution {eq}\displaystyle \; u = \sin x \; {/eq}.
This gives us {eq}\displaystyle \; \, \cos x \,...
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Chapter 13 / Lesson 5Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples.