Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 4th power of the quantity negative 1 plus 3 times k over n and 3 over n as a definite integral.

Question

Write  as a definite integral.

Answer 1

lim ∑₁ⁿ(- 1 + 3k/n)⁴·3/n = ∫_-1²x⁴dx = x⁵/5_-1² = 32/5 + 1/5 = 33/5.

n → ∞