Integral of 1/(1+X^2) Using Geometric Approach – ATan ArcTan

Published by Fudgy McFarlen on June 26, 2014June 26, 2014

I had to do a trigonometric integral the other day and realized I should be able to see the integral at a glance instead of the mechanistic method I used by substituting x=tan(theta)

W={Delta}{theta}*z

Due to similarity of triangles

{z/1}={{Delta}x}/w

Substituting

{z/1}={{Delta}x}/{{Delta}{theta}*z}

${{Delta}x}/z^2={Delta}{theta}$

${{Delta}x}/{1+x^2}={Delta}{theta}$

$int{.}{.}{.}{{Delta}x}/{1+x^2}=int{.}{.}{.}{Delta}{theta}$

$int{.}{.}{.}{{Delta}x}/{1+x^2}={theta}=atan(x)$

Related Topic

Area of the Rectangle Puzzle

Calculus Proof of the Pythagorean Theorem

Integral of 1/(1+X^2) Using Geometric Approach – ATan ArcTan

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