NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

If ∫ 0 1 x 11 e - x 24 d x = A , and ∫ 0 1 x 3 e - x 8 d x = B, then the relation between A and B is

Options

AA = 3 B
BB = 3 A
CA + 3 B = 0
DB + 3 A = 0

Correct answer

B. B = 3 A

Step-by-step solution

In A , let x 12 = t ⇒ 12 x 11 d x = d t ⇒ A = 1 12 ∫ 0 1 e - t 2 d t In B , let x 4 = u ⇒ 4 x 3 d x = d u ⇒ B = 1 4 ∫ 0 1 e - u 2 d x = 1 4 ∫ 0 1 e - t 2 d t ⇒ B = 1 4 12 A ⇒ B = 3 A

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