Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN: 9781133382119

Author: Swokowski

Publisher: Cengage

*expand_more*

*expand_more*

*format_list_bulleted*

#### Concept explainers

Question

The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x)=(x^2)/(12) f(x)=(x^2)/(12) on the interval [2,6].

The value of this left endpoint Riemann sum is __________________ , the area of the region enclosed by y=f(x)y=f(x), the x-axis, and the vertical lines x = 2 and x = 6.

Expert Solution

Trending nowThis is a popular solution!

Step by stepSolved in 4 steps with 4 images

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions

Consider the function f(x) = 4x2 −x3.
Provide the graph of the region bounded by f(x) and the x-axis over the interval [0, 4].
Which type of Riemann sum (left or right) gives a better estimate for the area of this region? Use n=5 intervals to find the left and right endport Riemann Sum. Please provide all of your work. Justify your answer.
You may use the graphing calculator to facilitate the calculation of the Riemann sum, or the webtool. Use four decimal places in all your calculations.

*arrow_forward*

1. Approximate the area under f(x)=3x^2 +1 on [-5,0] using RIGHT Riemann sum with 5 approximating rectangles.
2. Approximate the area under f(x)=3x^2 +1 on [-5,0] using LEFT Riemann sum with 5 approximating rectangles.
Can you please use sigma notations (example included)

*arrow_forward*

Use a Riemann sum with 3 subdivisions and right-hand endpoints to find an approximation for the area under the curve
y=ln(x^2+1)
and above the x-axis from x=1 to x=7. Round to three decimal places THIS TWO PLEASE
The Riemann sum approximation with 3 subdivisions and using the right endpoints is
A.
Equal to exact area
B.
Smaller than exact area
C.
Greater than exact area

*arrow_forward*

Consider the function f(x)=x2 on the interval [0,8]. Let P be a uniform partition of [0,8] with 20 sub-intervals. Compute the left and right Riemann sum of f on the partition. Use exact values.
compute and explain step by step please

*arrow_forward*

(a) Estimate the area under the graph of the function f(x)=1/x+4 from x=0 to x=1 using a Riemann sum with n=10 subintervals and right endpoints.
Round your answer to four decimal places.
area =
(b) Estimate the area under the graph of the function f(x)=1/x+4 from x=0 to x=1 using a Riemann sum with n=10 subintervals and left endpoints.
Round your answer to four decimal places.
area =

*arrow_forward*

Left and right Riemann sums Let R be the region bounded by the graphthe x-axis between x = 4 and x = 16.with ƒ(x) = 1/x, does the left Riemannsum or the right Riemann sum overestimate the area under the curve?

*arrow_forward*

Suppose a left Riemann sum is used to approximate the area of the regionbounded by the graph of a positive function and the x-axis on theinterval [a, b]. Fill in the table to indicate whether theresulting approximation underestimates or overestimates the exactarea in the four cases shown. Use a sketch to explain your reasoningin each case.

*arrow_forward*

Find an area similar to the example f(x)=x^2 from [0,1] that we couldn't have computed from geometry. Use Riemann sums to calculate (limits, etc). Area cannot simply be a rectangle, triangle or a circle (as this is a calculus problem). Give a detailed explanation and show all work.

*arrow_forward*

Find the area (in square units) of the region under the graph of the function f on the interval [−6, 11], using the Fundamental Theorem of Calculus. Then verify your result using geometry.
f(x)=8
______ square units

*arrow_forward*

fomular f(x) =tanx/x and has a hole at x=0 prove algebricaly that it has a hole at x=0

*arrow_forward*

Can you help me with this Thank you
Riemann sum for f(x) =2x on the interval [ 1,3].
The value of this Riemann sum is _____

*arrow_forward*

a) Express the integral as a Riemann sum.b) Graphf x( )then draw and shade the right endpoint rectangles, ? = 4, that estimate the bounded by f x( )and the x-axis on the given interval.c) Approximate the area of the shaded region by using the Midpoint Rule with n = 4.

*arrow_forward*

*arrow_back_ios*

- SEE MORE QUESTIONS

*arrow_forward_ios*

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage