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JEE Advanced2018MathematicsDefinite IntegrationActual

The value of the integral ∫ 0 1 2 1 + 3 x + 1 2 1 - x 6 1 4 d x is

Correct answer

0

Step-by-step solution

∫ 0 1 2 1 + 3 d x 1 + x 2 1 - x 6 1 4 ∫ 0 1 2 1 + 3 d x 1 + x 2 1 - x 6 1 + x 6 1 4 Put 1 - x 1 + x = t ⇒ - 2 d x 1 + x 2 = d t I = ∫ 1 1 3 1 + 3 d t - 2 t 6 4 = - 1 + 3 2 × - 2 t 1 1 3 = 1 + 3   3 - 1 = 2

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