Write the definite integral for the summation

Question

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Answer 1

I nterval of integration is [2, 3]. Because if k = 0 we get 2+ 0/n = 2, if k = n then we get 2 + n/n = 3.

This is lim of right integral sum for f(x) = x³_{. This limit is equal} ∫₂³x³dx = x⁴/4|₂³= 3⁴/4 - 2⁴/4 = 81/4 - 16/4 = 65/4

Answer 2

The integral from 0 to 1 of (2+x)³ dx.