Given f(x) = x^2 + 3, find the exact area A of the region under f(x) on the interval [1, 3] by first computing
n
Σf(xi)Δx and then taking the limit as n-->∞.
i=1

Please see the attached file for the fully formatted problems.

Finding Area Using Sums and Limits is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Evaluate
(lim)(sin(Pi/(n))+sin((2*Pi)/(n))+sin((3*Pi)/(n))+***+sin((n*Pi)/(n)))/(n)
by interpreting it as the limit of Riemann sums for a continuous function f defined on [0,1].
keywords: integration, integrates, integrals, integrating, double, triple, multiple

(a) Consider the attached limit of summed terms
(i) Explain why each of the sums in the attached expression gives an over-estimate of the area beneath the curve {see attachment}
(ii) Evaluate this limiting sum, using the expression {see attachment}
(iii) Check your answer in (ii), by using the fundamental theorem

Consider the function f(x) = x^2 + 2 on the closed interval [1, 6]. Using rectangles, use n = 10 and calculate the approximate area between the function f and the x axis on the interval [1, 5]. Use left endpoints in the following.
1. Find the change in x for each sub-interval.
2. Find f(1); f(1.5); f(2); f(2.5); f(3) . .

Give the following table of values determine by the empirical (ie: the Riemann left and right handsums) method the area under the function between X=0 and X=70. (hint: use n=7)
X 0 10 20 30 40 50 60 70
Y 700 400 300 400 700 1200 1900 2800
A. Graph the function over these x values and explain in your own words what the r

** Please see the attached file for a Word formatted copy of the problem description **
1. let f(x) = x^2-2x+2 on the interval [-1, 2]. Sketch a graph of this function along with the rectangles that would be used to approximate the area under the curve using a right sum with n = 6. Be accurate and make your graph large.
a) C

Using the formula for the surface area of a revolving curve about the x-axis:
S=∫2πy√(1 + (dy/dx)²)dx throughout a,b
Find the area of the surface generated by revolving the curve about the x axis within the given boundaries
y=√(x + 1)
1≤x≤5
Please be detailed, showing the compl

12) What is limit as h approaches 0 of [cos(pi/2 + h) - cos(pi/2)] / [h]
Ans is -1. Explain.
14) The area of the region in the first quadrant between the graph of y=x times the
sqrt of (4-x^2) and the x axis is? Ans is 8/3. Explain.
15) If x^2 + y^3 = x^3y^2, then dy/dx = ? Explain.
Ans is [3x^2y^2 - 2x]

Fay Ling is not going to pass her second semester math class unless she can supply the missing addends andsums in the following grid. Please help her by filling in the missing information (please see attached).