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Chapter 5: Q. 19 (page 464)

Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.

Short Answer

Expert verified

Ans:

$\int \frac{x}{\sqrt{x^{2} - 1}} d x f o r 41 \int x \sqrt{x^{2} + 1} d x f o r 42 \int \frac{x^{2} + 9}{x^{\frac{3}{2}}} d x f o r 46$

Step by step solution

01

Step 1. Given information:

Use trigonometric substitution

02

Step 2. Finding the three integrals using trigonometric substitution :

The three integrals that can be solved without using a trigonometric substitution are exercises 41,42 and 46.

The integrals are as follows.

41. $\int \frac{x}{\sqrt{x^{2} - 1}} d x$

42. $\int x \sqrt{x^{2} + 1} d x$

46. $\int \frac{x^{2} + 9}{x^{\frac{3}{2}}} d x$

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Most popular questions from this chapter

For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.

$\int \sin u d u$

Solve the integral: $\int \frac{3 x + 1}{x} d x$

Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) An integral with which we could reasonably apply trigonometric substitution with $x = \tan u$ .

(b) An integral with which we could reasonably apply trigonometric substitution with $x = 4 \sec u$ .

(c) An integral with which we could reasonably apply trigonometric substitution with $x - 2 = 3 \sin u$ .

Solve the integral: $\int (3 - x) e^{2 x} d x$

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.

$u (x) = \sin x$

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