An archive the questions from Mark's Fall 2018 Calc I Course.

Computing a Riemann sum

Mark

(10 pts)

Use your initials to create a fun function of the form

f(x) = \sin(F x^2 + M x + L),

where F, M, and L refer to the position in the alphabet of your first, middle, and last initials. For example, my initials are MCM so my function is

f(x) = \sin(13x^2 + 3x + 13).

Now, let’s find some Riemann sums estimating

\int_{-1}^1 f(x) dx.

Specifically:

  1. Type out the left Riemann sum corresponding to n=4 terms.
  2. Use a calculator or computer to evaluate that sum.
  3. Use a computer to evaluate the Riemann sum with n=400 terms. For example, here’s how I’d find the left Riemann sum with 100 terms for my function.
audrey

My initials are AEM so my funcrion is f(x) = sin(x^2 + 5x+13).

So my sum is
sin(9)1/2 + sin(13-9/4)1/2 + sin(13)1/2 + sin(13+13/4)1/2.

SMP

My initials are SMP so my function is f(x)=sin(19x^2+13x+16)
So my sum is

sin(22)1/2+sin(14.25)1/2+sin(16)1/2+sin(27.25)1/2

Evaluating my Riemann sum I got 0.428561811856487

AFRO

My initials are J.E.B meaning my function would be

  1. f(x)= sin(10x^2+5x+2)

2.sin(7)1/2+sin2 (7/4)1/2+ sin(2)+sin 7(1/2)

  1. my evalution ofr n= 400 terms 0.42
IamGamerGod

My initials are BLG so my function is f(x)= sin(2x^2+12x+7) therefore my sum is

sin(-3)(1/2)+sin(1.5)(1/2)+sin(13.5)(1/2)+sin(21)(1/2)

Evaluating my Riemann Sum I got -0.0925504935852849

haleymlindsey

My initials are HML so my function is f(x) = sin(8x^2 + 13x +12)

Therefore, my sum is sin(7)1/2 + sin(15/2)1/2 + sin(12)1/2 + sin(41/2)1/2

Evaluating the Riemann sum with n = 400 gives me 0.387635635905362

aallen8

My initials are AHA so my function is f(x)=sin(x^2+8x+1) so my sum is sin(-6)1/2+sin(-11/4)1/2+sin(21/4)1/2+sin(10)1/2
With n=400 I got 0.248077053856657

hgregory

My initials are HDG so my function is

  1. f(x)=sin(8x^2+4x+7)

  2. sin(11)(1/2)+sin(7)(1/2)+sin(7(1/2)+sin(11)(1/2)

  3. Evaluating the Riemann sum of n=400 results in .483513031336131

Cottoncandy

My initial are MEA so my function is f(x)=sin(13x^2+5x+1)

So my sum is sin(9)(1/2)+sin(1.75)(1/2)+sin(6.75)(1/2)

Evaluating the Riemann sum when n=400 the sum is 0.48475762951390

hgriffin

My initials are HKG, so my function is f(x)=sin(8x^2+11x+6)

My sum is sin(3)1/2+sin(5/2)1/2+sin(6)1/2+sin(27/2)1/2

After evaluating with n=400 I got 0.194468165373155

jcox

My initials are CJK, so my function is f(x)=sin(3x^2+10x+11).
My sum is sin(4)1/2+sin(27/4)1/2+sin(11)1/2+sin(67/4)1/2.
The value of the sum for n=4 terms, shown above, is -1.0851.
The value of the sum for n=400 terms is -0.2041.

Serb

My initials are NRC so my function is f(x)=sin(14x^2+18x+4)
So my sum is
sin(0)1/2+sin(-6/4)1/2+sin(4)1/2+Sin(16.5)1/2
Evaluating my Riemann sum I got -0.482725583702569