Question

If `int_0^a dx/(1 + 4x^2) = π/8`, then find the value of a.

Answer 1

`int_0^a dx/(1 + 4x^2) = π/8`

`int_0^a dx/(1 + (2x)^2) = π/8`   ...`[int 1/(1 + x^2) dx = tan^-1x + C]`

`1/2 [tan^-1 (2x)]_0^a = π/8`

`tan^-1 2a - tan^-1 0 = π/8 xx 2`

`tan^-1 2a - 0 = π/4`

`2a = tan  π/4`

2a = 1

a = `1/2`