\( y = x^n \)
Riemann Sum
\[ \int_0^1 x^2 \, dx = \frac{1}{3} \]
\[ S_N = \sum_{i=1}^{N} \left( \frac{i}{N} \right)^n \cdot \frac{1}{N} \]
Riemann Sum
0.385000
Exact Value
0.333333
Absolute Error
0.051667
Relative Error
15.50%
Mathematical Background
The integral \( \displaystyle\int_0^1 x^n \, dx = \frac{1}{n+1} \) is approximated by dividing \([0,1]\) into \(N\) equal subintervals and summing rectangle areas. As \(N \to \infty\), the Riemann sum converges to the exact value.