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JEE Advanced2006MathematicsDefinite IntegrationActual

The value of (5050) ₀^1 (1-x⁵⁰ )¹⁰⁰ d x ₀^1 (1-x⁵⁰ )¹⁰¹ d x

Correct answer

0

Step-by-step solution

Let I₂= ₀^1 (1-x⁵⁰ )¹⁰¹ d x , using integration by parts aligned & .= [(1-x)⁵⁰ )¹⁰¹ x ]₀^1+ ₀^1 (1-x⁵⁰ )¹⁰⁰ 50 x⁴⁹ x d x & =0- ₀^1(50)(101) (1-x⁵⁰ )¹⁰⁰(-x)⁵⁰ d x & =-(50)(101) ₀^1 (1-x⁵⁰ )¹⁰¹ d x+(50)(101) ₀^1 (1-x⁵⁰ )¹⁰⁰ d x & =5050 I₂+5050 I₁ aligned aligned & I₂+5050 I₂ & =5050 I₁ & (5050) I₁ I₂ & =5051 aligned

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