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Evaluate Exercise 9 by reversing the order of itnegraiton. (There will be two integrals, why?)

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

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12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Evaluate the integrals in …

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Evaluate ∫ 𝑑𝑥 /9 + 𝑥 2

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In Exercises $9-46,$ evalu…

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Evaluate the following int…

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$$\text {Evaluate the foll…

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Let'S talk about question number 74 point, so this can be rewritten as d x over right. Let'S take the 3 outside. So when we take 3 outside, we have 9 over 3 plus x square integral, so we have over here as 1 over 3. This will be d x over 3 plus x, squared integral this can further be written as 1 over 3 times integral of d x over x square plus. This can be written as root 3 square. Now we have a formula that d x over x, squared plus a square integral, is 1 over a tan inverse x over a plus c. So using that we write this 1 as 1. Over 3 is, as it is, 1 over a is root, 3, so 1. Over root 3 tan inverse x over a which is again root, 3 plus some constant c. So finally, it becomes tan inverse x over root 3 over 3 root, 3 plus c. This is the final answer:

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