Chapter 5: Q. 81 (page 465)

Solve given definite integral.
${鈭�}_{4}^{5} 鈥� \frac{1}{x \sqrt{x^{2} + 9}} d x$

Short Answer

Expert verified

$鈭� \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{5}) + \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{4}) .$

Step by step solution

Step1. Given Information

The integral is as follow.

${鈭�}_{4}^{5} 鈥� \frac{1}{x \sqrt{x^{2} + 9}} d x$

The objective is to solve the integral.

Step2. Solution

The definite integral is solved below.

$\begin{array}{l} {鈭�}_{4}^{5} 鈥� \frac{1}{x \sqrt{x^{2} + 9}} d x \\ = {[鈭� \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{x})]}_{4}^{5} \\ = [鈭� \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{5})] 鈭� [鈭� \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{4})] \\ = 鈭� \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{5}) + \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{4}) \end{array}$

Therefore, the value is $鈭� \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{5}) + \frac{1}{3} \sinh^{鈭� 1} 鈦� (\frac{3}{4}) .$

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Solve given definite integral.
${鈭�}_{4}^{5} 鈥� \frac{1}{x \sqrt{x^{2} + 9}} d x$

Short Answer

Step by step solution

Step1. Given Information

Step2. Solution

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91影视

Solve given definite integral.鈭�45鈥�1xx2+9dx

Short Answer

Step by step solution

Step1. Given Information

Step2. Solution

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Most popular questions from this chapter

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Solve given definite integral.
${鈭�}_{4}^{5} 鈥� \frac{1}{x \sqrt{x^{2} + 9}} d x$