Find the value of the definite integral using sums, not antiderivatives:

int= integral sign

int((x + 2)/(x^(3/2)),x= 16..25)dx

Please help.

To find the value of the definite integral using sums, you can use the concept of Riemann sums. The key idea is to divide the interval [16, 25] into smaller subintervals and approximate the integral as the sum of areas of rectangles.

1. Determine the number of subintervals (n): In this case, we want to divide the interval into n equal subintervals. We can choose a value for n, which will depend on how accurately you want to approximate the integral. Let's assume n = 10 for now.

2. Find the width of each subinterval (Δx): Divide the length of the interval by the number of subintervals. In this case, the interval length is (25 - 16) = 9, so Δx = 9/n.

3. Choose sample points within each subinterval: To evaluate the function within each subinterval, choose a sample point. You can either choose the left endpoint, right endpoint, or the midpoint of each subinterval. Let's use the midpoint.

4. Set up the Riemann sum: The Riemann sum is the sum of the areas of rectangles formed within each subinterval. The area of each rectangle can be approximated as f(x) * Δx, where f(x) is the function evaluated at the sample point within each subinterval.

5. Evaluate the Riemann sum: Plug in the chosen sample point into the function, multiply by Δx, and sum up all the individual areas.

In this case, the function is (x + 2) / (x^(3/2)). Follow the steps above to approximate the definite integral within the given limits of integration [16, 25].