Consider the function f(x) = -x + 8 over the interval [2, 7). Problems 1-4, Approximate the area between the graph of f (x) and the x-axis over the given inter- val by summing the area of the given...

Extracted text: Consider the function f(x) = -x + 8 over the interval [2, 7). Problems 1-4, Approximate the area between the graph of f (x) and the x-axis over the given inter- val by summing the area of the given number of rectangles and the given condition for finding the height of each rectangle. Make sure to draw each rectangle on the graph. 1. Use n = 5 rectangles and use the LEFT endpoint of each subinterval for the height. 2. Use n = 5 rectangles and use the RIGHT endpoint of each subinterval for the height. 3. Use n = 10 rectangles and use the LEFT endpoint of each subinterval for the height. 4. Use n = 10 rectangles and use the RIGHT endpoint of each subinterval for the height. 5. Find a formula in terms of n (an arbitrary number of rectangles) that would give the approximate area between the graph of f(x) and the x-axis over the given interval. Use the Right endpoint of each subinterval to calculate the height. 6. Use the result of the previous problem to approximate the area using n = 100 rectangles. 7. Find the exact area by finding the limit as n → o of the result of problem 5. 8. Find the antiderivative F(x) of f(x) = -x + 8. Compute F(7) – F(2).