How do you do this question?

20

Step-by-step explanation:

A left Riemann sum approximates a definite integral as:

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

there are infinitely many solutions.