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Question
`int_0^1 x^2/(1 + x^2)dx` = ______.
Options
`π/4 - 1`
`π/2 - 1`
`1 - π/2`
`1 - π/4`
MCQ
Fill in the Blanks
Solution
`int_0^1 x^2/(1 + x^2)dx` = `underlinebb(1 - π/4)`.
Explanation:
`int_0^1 x^2/(1 + x^2)dx = int_0^1 (1 + x^2 - 1)/(1 + x^2)dx`
= `int_0^1 ((1 + x^2)/(1 + x^2) - 1/(1 + x^2))dx`
= `int_0^1 (1 - 1/(1 + x^2))dx`
= `[x - tan^-1x]_0^1`
= `1 - tan^-1 1`
= `1 - π/4`
shaalaa.com
Methods of Evaluation and Properties of Definite Integral
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