A) Evaluate the integral: integral of (x + 4)/(x^2 + 4) dx. B) Evaluate the integral: integral...


A) Evaluate the integral: {eq}\int \frac{x + 4}{x^2 + 4} \, \mathrm{d}x {/eq}.

B) Evaluate the integral: {eq}\int_{0}^{\frac{\pi}{2}} \sqrt{1 - \cos \theta} \; \mathrm{d} \theta {/eq}.

Techniques for Integrals:

Evaluating integrals sometimes require recognizing familiar forms of derivatives of known functions. Will a substitution work? If it's close, maybe there is something we can do to make it so that a substitution works. Or maybe we can expand the integrand to make integration easier. Identities and simplifying the integrand might also work. All techniques we have can solve a lot of different integrals, and combinations of them even more.

Answer and Explanation: 1

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(A) For the integral $$\int \frac{x + 4}{x^2 + 4} \, \mathrm{d}x $$ we can divide each term and get $$\int \frac{x + 4}{x^2 + 4} \, \mathrm{d}x =...

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How to Calculate Derivatives of Inverse Trigonometric Functions


Chapter 8 / Lesson 12

A methodology to learn in maths is the functions of the inverse trigonometric function to calculate distances and angles. Learn more about how to calculate derivatives of inverse trigonometric and it's functions.

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