Q. 66 Solve each of the integrals. Som... [FREE SOLUTION]

Chapter 5: Q. 66 (page 465)

Solve each of the integrals. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
$鈭� \sqrt{x^{2} - 2} d x$ .

Short Answer

Expert verified

The value is, $- \cos h^{- 1} (\frac{\sqrt{2} x}{2}) + \frac{1}{2} \sin h (2 \cos h^{- 1} (\frac{\sqrt{2} x}{2})) + C$ .

Step by step solution

Step 1. Given Information.

The integral is,

$鈭� \sqrt{x^{2} - 2} d x$ .

Step 2. Simplifying the integral.

Let

Step 3. Solving the Integral.

The solution of integral,

$鈭� \sqrt{x^{2} - 2} d x = 鈭� 2 \sin h^{2} (u) d u = 2 鈭� (\frac{1}{2} \cos h (2 u) - \frac{1}{2}) d u = - 鈭� d u + 鈭� \cos h (2 u) d u = - u + \frac{1}{2} 鈭� \cos h (v) d v [v = 2 u, d v = 2 d u] = - u + \frac{1}{2} \sin h (v) + C = - u + \frac{1}{2} \sin h (2 u) + C = - \cos h^{- 1} (\frac{\sqrt{2} x}{2}) + \frac{1}{2} \sin h (2 \cos h^{- 1} (\frac{\sqrt{2} x}{2})) + C$

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91影视

Solve each of the integrals. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
$鈭� \sqrt{x^{2} - 2} d x$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplifying the integral.

Step 3. Solving the Integral.

One App. One Place for Learning.

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91影视

Solve each of the integrals. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.鈭�x2-2dx.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Simplifying the integral.

Step 3. Solving the Integral.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Calculus

Mechanics Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each of the integrals. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
$鈭� \sqrt{x^{2} - 2} d x$ .