Answer:
20
Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
[tex]\int\limits^b_a {f(x)} \, dx \approx \sum\limits_{k=1}^{n}f(x_{k}) \Delta x \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times (k-1)[/tex]
Here, the integral is ∫₀² 9ˣ dx, and the number of subintervals is n = 4.
So Δx = 2/n = 1/2, and x = 2(k−1)/n = (k−1)/2.
Plugging in:
∑₁⁴ 9^((k−1)/2) (1/2)
1/2 ∑₁⁴ 9^((k−1)/2)
1/2 (9^((1−1)/2) + 9^((2−1)/2) + 9^((3−1)/2) + 9^((4−1)/2))
1/2 (9^(0) + 9^(1/2) + 9^(1) + 9^(3/2))
1/2 (1 + 3 + 9 + 27)
20
