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Chapter 5: Q 22. (page 452)

Solve the integral.
$鈭� \cos^{2} x d x$

Short Answer

Expert verified

Answer is $\begin{array}{rcl} \frac{x}{2} + \frac{\sin 2 x}{4} + C \end{array}$

Step by step solution

01

Step 1. Given information

An integral is $鈭� \cos^{2} x d x$

02

Step 2. Explanation

Consider the integral $鈭� \cos^{2} x d x$

Use the formula: $\cos^{2} x = \frac{1 + \cos 2 x}{2}$

So,

$\begin{array}{rcl} 鈭� \cos^{2} x d x & = & 鈭� \frac{1 + \cos 2 x}{2} d x \\ = & \frac{x}{2} + \frac{\sin 2 x}{4} + C \end{array}$

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Most popular questions from this chapter

Solve the integral

$鈭� \sqrt{3 - x} \sqrt{x - 1} d x$

Solve the integral: $鈭� \frac{x}{e^{x}} d x$

Explain how to use long division to write the improper fraction $\frac{172}{5}$ as the sum of an integer and a proper fraction.

Problem Zero: Read the section and make your own summary of the material.

Solve given definite integral.

${鈭�}_{1 / 4}^{1 / 2} 鈥� \frac{1}{x^{2} \sqrt{1 鈭� x^{2}}} d x$

See all solutions

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