f(x)=sqrt(X); x1=0, x2=9, n=9, h=1; f(0)=0
Left Riemann: i, x, f(x) × h
1, 0, 0 × 1 = 0
2, 1, 1 × 1 = 1
3, 2, 1.41421356 × 1 = 1.41421356
4, 3, 1.73205081 × 1 = 1.73205081
5, 4, 2 × 1 = 2
6, 5, 2.23606798 × 1 = 2.23606798
7, 6, 2.44948974 × 1 = 2.44948974
8, 7, 2.64575131 × 1 = 2.64575131
9, 8, 2.82842712 × 1 = 2.82842712
Total: 16.30600052603572
Midpoint: i, x, f(x) × h
1, 0.5, 0.70710678 × 1 = 0.70710678
2, 1.5, 1.22474487 × 1 = 1.22474487
3, 2.5, 1.58113883 × 1 = 1.58113883
4, 3.5, 1.87082869 × 1 = 1.87082869
5, 4.5, 2.12132034 × 1 = 2.12132034
6, 5.5, 2.34520788 × 1 = 2.34520788
7, 6.5, 2.54950976 × 1 = 2.54950976
8, 7.5, 2.73861279 × 1 = 2.73861279
9, 8.5, 2.91547595 × 1 = 2.91547595
Total: 18.053945891265528
Right Riemann: i, x, f(x) × h
0, 1, 1 × 1 = 1
1, 2, 1.41421356 × 1 = 1.41421356
2, 3, 1.73205081 × 1 = 1.73205081
3, 4, 2 × 1 = 2
4, 5, 2.23606798 × 1 = 2.23606798
5, 6, 2.44948974 × 1 = 2.44948974
6, 7, 2.64575131 × 1 = 2.64575131
7, 8, 2.82842712 × 1 = 2.82842712
8, 9, 3 × 1 = 3
Total: 19.30600052603572
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Answers & Comments
f(x)=sqrt(X); x1=0, x2=9, n=9, h=1; f(0)=0
Left Riemann: i, x, f(x) × h
1, 0, 0 × 1 = 0
2, 1, 1 × 1 = 1
3, 2, 1.41421356 × 1 = 1.41421356
4, 3, 1.73205081 × 1 = 1.73205081
5, 4, 2 × 1 = 2
6, 5, 2.23606798 × 1 = 2.23606798
7, 6, 2.44948974 × 1 = 2.44948974
8, 7, 2.64575131 × 1 = 2.64575131
9, 8, 2.82842712 × 1 = 2.82842712
Total: 16.30600052603572
Midpoint: i, x, f(x) × h
1, 0.5, 0.70710678 × 1 = 0.70710678
2, 1.5, 1.22474487 × 1 = 1.22474487
3, 2.5, 1.58113883 × 1 = 1.58113883
4, 3.5, 1.87082869 × 1 = 1.87082869
5, 4.5, 2.12132034 × 1 = 2.12132034
6, 5.5, 2.34520788 × 1 = 2.34520788
7, 6.5, 2.54950976 × 1 = 2.54950976
8, 7.5, 2.73861279 × 1 = 2.73861279
9, 8.5, 2.91547595 × 1 = 2.91547595
Total: 18.053945891265528
Right Riemann: i, x, f(x) × h
0, 1, 1 × 1 = 1
1, 2, 1.41421356 × 1 = 1.41421356
2, 3, 1.73205081 × 1 = 1.73205081
3, 4, 2 × 1 = 2
4, 5, 2.23606798 × 1 = 2.23606798
5, 6, 2.44948974 × 1 = 2.44948974
6, 7, 2.64575131 × 1 = 2.64575131
7, 8, 2.82842712 × 1 = 2.82842712
8, 9, 3 × 1 = 3
Total: 19.30600052603572