Chapter 5: Q. 85 (page 465)

Solve given definite integral.
${鈭�}_{1}^{2} 鈥� \frac{3}{{(9 鈭� 2 x^{2})}^{3 / 2}} d x$

Short Answer

Expert verified

$\frac{2}{3} 鈭� \frac{\sqrt{7}}{21}$

Step by step solution

Step1. Given Information

The integral is as follows.

${鈭�}_{1}^{2} 鈥� \frac{3}{{(9 鈭� 2 x^{2})}^{\frac{3}{2}}} d x$

The objective is to solve the integral.

Step2. Assumptions

To solve the integral, let $u = x^{2}$

Now, derivation of above equation is solved below.

$u = x^{2} d u = 2 x d x$

Step3. Solution

The integral is solved below.

$\begin{aligned} 鈭� \frac{3}{{(9 鈭� 2 x^{2})}^{\frac{3}{2}}} d x \\ = \frac{x}{3 \sqrt{9 鈭� 2 x^{2}}} \end{aligned}$

Step4. Solution

The definite integral is solved below.

${鈭�}_{1}^{2} 鈥� \frac{3}{{(9 鈭� 2 x^{2})}^{\frac{3}{2}}} d x$

$= {[\frac{x}{3 \sqrt{9 鈭� 2 x^{2}}}]}_{1}^{2}$

$= [\frac{2}{3 \sqrt{9 鈭� 2 (2)^{2}}}] 鈭� [\frac{1}{3 \sqrt{9 鈭� 2 (1)^{2}}}]$

$= \frac{2}{3} 鈭� \frac{\sqrt{7}}{21}$

Therefore, the value is $\frac{2}{3} 鈭� \frac{\sqrt{7}}{21}$

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91影视

Solve given definite integral.
${鈭�}_{1}^{2} 鈥� \frac{3}{{(9 鈭� 2 x^{2})}^{3 / 2}} d x$

Short Answer

Step by step solution

Step1. Given Information

Step2. Assumptions

Step3. Solution

Step4. Solution

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91影视

Solve given definite integral.鈭�12鈥�39鈭�2x23/2dx

Short Answer

Step by step solution

Step1. Given Information

Step2. Assumptions

Step3. Solution

Step4. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Calculus

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve given definite integral.
${鈭�}_{1}^{2} 鈥� \frac{3}{{(9 鈭� 2 x^{2})}^{3 / 2}} d x$