Answer Happy

For the entire lab, use the function f(x)=x+2−5sin(x) over the interval [-3,12]. Express all calculations in numerical form to at least three decimal places. Problem 1 Plot f(x) over the interval [−3,12] Problem 2 Find an approximation for the area under the graph of f with a Riemann sum using right endpoints and 10 rectangles of equal width. Problem 3 Find an approximation for the area under the graph of f with a Riemann sum using left endpoints and 10 rectangles of equal width. Problem 4 Find an approximation for the area under the graph of f with a Riemann sum using midpoints and 10 rectangles of equal width. Problem 5 Find the area under the graph of f by using a limit of Riemann sums as n→∞. Problem 6 Evaluate the definite integral ∫−312​f(x)dx Problem 7 Which approximation was the closest to the actual area?