Question

1) Using the right endpoint with n = 4, approximate the area
of the region bounded by ? = 2?2 + 3, and x axis for x between 1
and 3.

2) Use Riemann sums and the limit to find the area of the
region bounded by ?(?) = 3? − 4 and x-axis between x = 0 and x =
1

Answer #1

Find the area of the region bounded by the graph of f(x) = 4x^3 +
4x + 9 and the x axis between x=0 and x=2 using Riemann sums.

Use the midpoint rule with 4 rectangles to approximate the area
of the region bounded above by y=sinx, below by the ?x-axis, on
the left by x=0, and on the right by ?=?

Estimate the area of the region bounded between the curve f(x) =
1 x+1 and the horizontal axis over the interval [1, 5] using a
right Riemann sum. Use n = 4 rectangles first, then repeat using n
= 8 rectangles. The exact area under the curve over [1, 5] is ln(3)
≈ 1.0986. Which of your estimates is closer to the true value?

Use upper and lower sums (left and right Riemann sums) to
approximate the area
of the region below y =sqrt(8x) using 4 subintervals of each width.
Round to three
decimal places.

1- Find the area enclosed by the given curves.
Find the area of the region in the first quadrant bounded on the
left by the y-axis, below by the line above left
by y = x + 4, and above right by y = - x 2 + 10.
2- Find the area enclosed by the given curves.
Find the area of the "triangular" region in the first quadrant that
is bounded above by the curve , below by the curve y...

Consider the region bounded by f(x) = x^3 + x + 3 and y = 0 over
[−1, 2].
a) Find the partition of the given interval into n subintervals
of equal length. (Write ∆x, x0, x1, x2, · · · , xk, · · · ,
xn.)
b) Find f(xk), and setup the Riemann sum ∑k=1 f(xk)∆x.
c) Simplify the Riemann sum using the Power Sum Formulas.
d) Find the area of the region by taking limit as n...

Let R be the region bounded above by f(x) = 3 times the (sqr
root of x) and the x-axis between x = 4 and x = 16. Approximate the
area of R using a midpoint Riemann sum with n = 6 subintervals.
Sketch a graph of R and illustrate how you are approximating it’
area with rectangles. Round your answer to three decimal
places.

Instructions: Approximate the following definite integrals using
the indicated Riemann sums.
1. Z 9 1 x 1 + x dx using a left-hand Riemann sum L4 with n = 4
subintervals.
2. Z 3 0 x 2 dx using a midpont Riemann sum M3 using n = 3
subintervals.
3. Z 3 1 f(x) dx using a right-hand Riemann Sum R4, with n = 4
subintervals

use the limit of a sum process to find the net area of the
region bounded by the curve y=x(3x-4) and the lines x=1, x=3 and
y=0 (note: you do not need to find the actual area of that
region

For the function f(x) = x, estimate the area of the region
between the graph and the horizontal axis over the interval 0≤x≤4
using a .
a. Riemann Left Sum with eight left rectangles.
b. Riemann Right Sum with eight right rectangles.
c. A good estimate of the area.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 17 minutes ago

asked 18 minutes ago

asked 41 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago