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Evaluate the integral. {eq}\int^\sqrt3_1 arctan (\frac{1}{x})dx {/eq}

Question:

Evaluate the integral. {eq}\int^\sqrt3_1 arctan (\frac{1}{x})dx {/eq}

Integration by parts

Let {eq}p{/eq} and {eq}q{/eq} is the function of {eq}x{/eq} then integration by parts;

{eq}\int {pqdx = p\int {qdx - \int {p'} \left( {\int {qdx} } \right)dx} } {/eq}

Chain rule:

Let {eq}p(x) {/eq} and {eq}q(x) {/eq} are the function of {eq}x {/eq} then the derivative of {eq}p(q(x)) {/eq} is given by chain rule ,such that ;

{eq}\frac{d}{{dx}}p(q(x)) = p'(q(x))\frac{d}{{dx}}q(x) {/eq}

Answer and Explanation: 1

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Given that: {eq}\displaystyle \int_1^{\sqrt 3 } a rctan(\frac{1}{x})dx {/eq}

{eq}\displaystyle\ \eqalign{ & \int_1^{\sqrt 3 } {ta{n^{ -...

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Definite Integrals: Definition

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Chapter 12 / Lesson 6
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A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.


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