4. Calculate the $\int_0^1 (4x^3 -3x^2)dx$ by definition of Riemann sum.

Hint: $\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$ and $\sum_{i=1}^n i^3 = \left[\frac{n(n+1)}{2}\right]^2$. (10%)

阿摩線上測驗 · 2026-10-22T13:43:06+08:00

4. Calculate the ∫_0^1 (4x^3 -3x^2)dx by definition of Riemann sum. Hint: Σ_i=1^n i^2 = (n(n+1)(2n+1))/6 and Σ_i=1^n i^3 = [(n(n+1))/2]^2. (10%)

4. Calculate the \(\int_0^1 (4x^3 -3x^2)dx\) by definition of Riemann sum.

Hint: $\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$ and $\sum_{i=1}^n i^3 = \left[\frac{n(n+1)}{2}\right]^2$. (10%)