Chapter 5: Q 14. (page 495)

Fill in the blanks to complete each of the following integration formulas.
$\int \sin^{- 1} x d x =_______$

Short Answer

Expert verified

The result is $x \sin^{- 1} x + \sqrt{1 - x^{2}} + C$ .

Step by step solution

Step 1. Given information.

Consider the given integration.

$\int \sin^{- 1} x d x$

Step 2. Find the integration.

Apply the by-parts integration method. Consider the values as $u = 1$ and $v = \sin^{- 1} x$ .

$\begin{array}{rcl} \int \sin^{- 1} x d x & = & x \sin^{- 1} x - \int \frac{x}{\sqrt{1 - x^{2}}} d x \\ = & x \sin^{- 1} x - \int \frac{x}{\sqrt{1 - x^{2}}} d x [t = 1 - x^{2}, - \frac{d t}{2} = x d x] \\ = & x \sin^{- 1} x - [- 2 \int \frac{1}{\sqrt{t}} d t] \\ = & x \sin^{- 1} x - [\frac{- 2 \sqrt{t}}{2}] \\ = & x \sin^{- 1} x + \sqrt{1 - x^{2}} + C \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Fill in the blanks to complete each of the following integration formulas.
$\int \sin^{- 1} x d x =_______$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the integration.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Decision Maths

Applied Mathematics

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following integration formulas.∫sin-1xdx=_______

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the integration.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Decision Maths

Applied Mathematics

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following integration formulas.
$\int \sin^{- 1} x d x =_______$