Final answer:
To compute the integral of the function f(x) = sin(x^2) between x = 1 and x = 2 using a Riemann sum, divide the interval [1, 2] into smaller subintervals and approximate the area under the curve by summing the areas of rectangles.
Step-by-step explanation:
To compute the integral of the function f(x) = sin(x^2) between x = 1 and x = 2 using a Riemann sum, we can divide the interval [1, 2] into smaller subintervals and approximate the area under the curve by summing the areas of rectangles with heights determined by the function. Let's say we divide the interval into n equally spaced subintervals.
The width of each subinterval is Δx = (2 - 1) / n = 1 / n. We can choose a sample point within each subinterval, let's call it xi. Then the height of each rectangle will be f(xi) = sin((xi)^2).
The Riemann sum is given by the formula: R_n = Σ[f(xi)Δx] from i = 1 to n. To compute the integral, we take the limit as n approaches infinity: ∫(1 to 2) sin(x^2) dx = lim(n→∞) R_n.