Evaluate the integral 4^ 3 x sec^2 (x^2) dx.


Evaluate the integral {eq}\displaystyle \ \int_{ \sqrt { \pi / 4 }}^{ \sqrt { \pi / 3 }} x \sec^2 (x^2) dx. {/eq}

Integration by Substitution:

Substitution is used to integrate functions that are compositions of other functions. Consider the term {eq}\sec^2 (x^2). {/eq} This is a composition of functions with inside function {eq}x^2. {/eq}

Try a substitution with {eq}u = x^2. {/eq} Then {eq}du =2x \, dx. {/eq}

Answer and Explanation:

Let {eq}u = x^2. {/eq} Then {eq}du =2x \, dx. {/eq} Rewrite the indefinite integral first.

{eq}\displaystyle \int x \sec^2 (x^2) \, dx \\ =...

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Learn more about this topic:

How to Solve Integrals Using Substitution

from Math 104: Calculus

Chapter 13 / Lesson 5

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