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Chapter 5: Q 37. (page 452)

Solve the following integral.

鈭�cos3xsin4xdx

Short Answer

Expert verified

Answer issin5x5-sin7x7+C

Step by step solution

01

Step 1. Given information

An integral is鈭�cos3xsin4xdx

02

Step 2. Explanation

鈭�cos3xsin4xdx=鈭�1-sin2xcosxsin4xdx

Let width="61">sinx=u

鈭�cos3xsin4xdx=鈭�u41-u2du=鈭�u4-u6du=u55-u77+C=sin5x5-sin7x7+C

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Most popular questions from this chapter

Domains and ranges of inverse trigonometric functions: For each function that follows, (a) list the domain and range, (b) sketch a labeled graph, and (c) discuss the domains and ranges in the context of the unit circle.

f(x)=sec鈭�1鈦�x

Suppose v(x) is a function of x. Explain why the integral

of dv is equal to v (up to a constant).

Solve the integral: 鈭�xsinxdx

Solve 鈭�x+2x2+4x32dxthe following two ways:

(a) with the substitution u=x2+4x;

(b) by completing the square and then applying the trigonometric substitution x + 2 = 2 sec u.

Complete the square for each quadratic in Exercises 28鈥�33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.

2(x+2)2
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