Question

Let f be the function given by f(x)= 9ˣ, if four subintervals of equal length are used, what is the value of the right riemann sum approximation for ∫20 f(x) dx

a. 20
b. 40
c. 60
d. 80

Answer 1

The value of the right Riemann sum approximation for ∫20 f(x) dx, where f(x) = 9ˣ and four subintervals of equal length are used, is 457,065.

Step-by-step explanation:

The problem asks us to find the value of the right Riemann sum approximation for the integral of the function f(x) = 9ˣ over the interval [0, 20] using four equal subintervals.

The right Riemann sum approximation divides the interval into subintervals and takes the right endpoint of each subinterval to calculate the height of the rectangle. The width of each rectangle is the length of the subinterval.

For this problem, since we have four subintervals, the length of each subinterval is (20-0)/4 = 5.

So, the right Riemann sum approximation is (f(5) + f(10) + f(15) + f(20)) * 5 = (9⁵ + 9¹⁰ + 9¹⁵ + 9²⁰) * 5 = 457,065.