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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let I = ∫_0^1 1 + x 1 - x dx and J = ∫_0^1 1 - x 1 + x dx then...

Let

I = \int_0^1 \sqrt{\frac{1 + \sqrt{x}}{1 - \sqrt{x}}} dx

and

J = \int_0^1 \sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} dx

then correct statement(s) is/are :

Options

A $I + J = 2$
B $I - J = \pi$
C $I = \frac{2 + \pi}{2}$
D $J = \frac{4 - \pi}{2}$ ***

Correct answer

B. $I - J = \pi$

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