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Home » Question: What is the value of the integral $\int_0^1 e^x \, dx$? - Parker Core Knowledge

Question: What is the value of the integral $\int_0^1 e^x \, dx$? - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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E(1) = E(0) + 1 = 1, \quad E(2) = 1 + (2\cdot1 + 1) = 1 + 3 = 4, \quad...
So $ E(n) = \sum_{k=0}^{n-1} (2k + 1) = n^2 $, since sum of first $ n...
Hence, $ E(10) = 10^2 = 100 $.
Question: An oceanographer models the depth $ d(t) $ (in meters) of a...
Solution: We are given that $ d(t) $ is a cubic polynomial satisfying:
d(1) = 1,\quad d(2) = 8,\quad d(3) = 27,\quad d(4) = 64.
Observe:
= 1^3,\quad 8 = 2^3,\quad 27 = 3^3,\quad 64 = 4^3.
So $ d(n) = n^3 $ for $ n = 1,2,3,4 $. Since $ d(t) $ is a cubic polyn...
d(t) = t^3.

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