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