I want to evaluate the following integral: ∫ − ∞ 0 R x 2 +...

2nalfq8

2nalfq8

Answered

2022-07-01

I want to evaluate the following integral:
0 R x 2 + R 2 3 d x

Answer & Explanation

Rafael Dillon

Rafael Dillon

Expert

2022-07-02Added 15 answers

The first approach gets 1 R π / 2 0 cos φ d φ = 1 R ; the second gets
1 R [ x ( x 2 + R 2 ) 1 / 2 ] 0 = 1 R lim x x ( x 2 + R 2 ) 1 / 2 = 1 R 1 = 1 R ,
contra your sign error. You mistakenly rewrote x ( x 2 + R 2 ) 1 / 2 , rather than ( 1 + R 2 / x 2 ) 1 / 2 , for x < 0. Bear in mind a 2 + b a = 1 + b / a 2 sgn a for a 0

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