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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View this answerGiven 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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Chapter 12 / Lesson 6A 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.