Answered: Find ∫ dx / √(4x2 + 1)

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter58: Achievement Review—section Five

Section: Chapter Questions

Problem 30AR: Determine dimension x to 3 decimal places.

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Question

Find ∫ dx / √(4x² + 1)

Expert Solution

Step 1

Given:

$\int \frac{1}{\sqrt{4 x^{2} + 1}} d x$

Step 2

It is given that,

$\int \frac{1}{\sqrt{4 x^{2} + 1}} d x$

On applying the Trigonometric substitution

$x = \frac{1}{2} tan(u)$

Then,

$\int \frac{1}{\sqrt{4 x^{2} + 1}} d x$ = $\int \frac{s e c (u)}{2} d u$

On taking the constant out,

$\int \frac{1}{\sqrt{4 x^{2} + 1}} d x$ = $\frac{1}{2} \int s e c (u) d u$ $\frac{1}{2} \ln |\tan (u) + s e c (u)|$

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Solve for x: z=x.
Determine dimension x to 3 decimal places.

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