NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

The value of lim n → ∞ Σ r = 1 r = 4 n n r 3 r + 4 n 2 is equal to

Options

A1 8
B1 10
C1 6
D1 9

Correct answer

B. 1 10

Step-by-step solution

lim n → ∞ Σ r = 1 r = 4 n 1 r / n 3 r n + 4 2 · 1 n = ∫ 0 4 1 x 3 x + 4 2 dx Put, 3 x + 4 = t 3 2 x dx = dt ⇒ 1 x dx = 2 3 dt when x = 0 then t = 4 when x = 4 then t = 10 = 2 3 ∫ 4 1 0 1 t 2 dt = 2 3 - 1 t 4 1 0 = - 2 3 1 1 0 - 1 4 = 1 1 0

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