Q24MP Find ddx鈭玹=1xt=2xcoshxttdt.... [FREE SOLUTION]

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Chapter 4: Q24MP (page 239)

Find $\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{c o s h x t}{t} d t$ .

Short Answer

Expert verified

The value of $\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t is 0$ .

Step by step solution

Given Information

Given that $\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t$ . ...(1)

Formula Used

We know that $\frac{d}{d x} {鈭�}_{u (x)}^{v (x)} f (x, t) d t = f (x, v) \frac{d v}{d x} - f (x, u) \frac{d u}{d x} + {鈭�}_{u}^{v} \frac{鈭� f}{鈭� x} d t$ ...(2)

Solving the given equation

Compare equation (1) and equation (2).

$\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = \frac{\cosh x (\frac{2}{x})}{\frac{2}{x}} 脳 \frac{d}{d x} (\frac{2}{x}) - \frac{\cosh x (\frac{1}{x})}{\frac{1}{x}} 脳 \frac{d}{d x} (\frac{1}{x}) + {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\sinh x t}{t} d t \frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = \cosh 2 脳 \frac{x}{2} (\frac{- 2}{x^{2}}) - \cosh 1 脳 (x) 脳 (\frac{- 1}{x^{2}}) + {(\frac{\cosh x t}{x})}_{\frac{1}{x}}^{\frac{2}{x}} \frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = (\frac{- 1}{x}) \cosh 2 - \cosh 1 (\frac{- 1}{x}) + \frac{1}{x} [\cosh x (\frac{2}{x}) - \cosh x (\frac{1}{x})]$

Solving Further,

$\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = (\frac{- 1}{x}) \cosh 2 - (\frac{- 1}{x}) \cosh 1 + \frac{1}{x} \cosh 2 - \frac{1}{x} \cosh 1 \frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = - \frac{1}{x} \cosh 2 + \frac{1}{x} \cosh 1 + \frac{1}{x} \cosh 2 - \frac{1}{x} \cosh 1 \frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = 0$

Hence the value of $\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{\cosh x t}{t} d t = 0$ .

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Find $\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{c o s h x t}{t} d t$ .

Short Answer

Step by step solution

Given Information

Formula Used

Solving the given equation

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91影视

Find ddx鈭�t=1xt=2xcoshxttdt.

Short Answer

Step by step solution

Given Information

Formula Used

Solving the given equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Work Energy and Power

Mechanics and Materials

Magnetism and Electromagnetic Induction

Fluids

Physics of Motion

Study anywhere. Anytime. Across all devices.

Find $\frac{d}{d x} {鈭�}_{t = \frac{1}{x}}^{t = \frac{2}{x}} \frac{c o s h x t}{t} d t$ .