How do you find b such that $intdx/(1+x^2)=pi/3$ from [0,b]?

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Answer 1 · 2016-10-30T01:01:13

$b=sqrt(3)$

You need to use the standard result $int 1/(1+x^2)dx = arctanx+C$

We have $int_0^b 1/(1+x^2)dx = pi/3$

$:. [arctanx]_0^b = pi/3$
$:. arctanb - arctan 0 = pi/3$
$:. arctanb - 0 = pi/3$
$:. arctanb = pi/3$
$:. b = tan(pi/3)$
$:. b = sqrt(3)$

How do you find b such that intdx/(1+x^2)=pi/3intdx/(1+x^2)=pi/3 from [0,b]?