Consider the function f(x)=sin⁡x on th interval [0, 3]. Let P be a uniform partition of [0, 3] with 4 sub-intervals. Compute the left and right Riemann sum of f on the partition. Enter approximate values, rounded to three decimal places.

Question

dieseisB · Accepted Answer

Let f(x) be defined on the closed interval [a,b] and let [a,b] is portioned into n subintervals. Then, the left Riemann sum is defined as ∑i=0n−1f(xi)Δx where xi is the left endpoint of each subinterval and the right Reimann sum is ∑i=0nf(xi)Δx where xi is the right endpoint of each subinterval. The function is (x)=sin⁡x on the interval [0, 3]. Here the interval is portioned into 4 subintervals. That is, n=4. Find the length of each subinterval Δ x as, Δx=b−an =3−04 =34 =0.75 Therefore the subintervals are, [0,0.75],[0.75,1.5],[1.5,2.25],[2.25,3]. Left sum: Find the left Reimann sum as follows. ∑i=0n−1f(xi)Δx=0.75(f(x+0)+f(x1)+f(x2)+f(x3)) =0.75(sin⁡(0)+sin⁡(0.75)+sin⁡(1.5)+sin⁡(2.25)) ≈1.843 Right sum: Find the Right Reimann sum as follows. ∑i=1nf(xi)Δx=0.75(f(x1)+f(x2)+f(x3)+f(x4)) =0.75(sin⁡(0.75)+sin⁡(1.5)+sin⁡(2.25)+sin⁡(3)) ≈1.949 Left sum: 1.843 Right sum: 1.949

Consider the function f(x) = sin x on th interval [0, 3]. Let P be a uniform partition of [0, 3] with 4 sub-intervals. Compute the left and right Riemann sum of f on the partition. Enter approximate values, rounded to three decimal places.

Answered question

Answer & Explanation

New Questions in College Statistics