(adsbygoogle = window.adsbygoogle || []).push({}); Need some urgent help with Riemann Sums.

1. The problem statement, all variables and given/known data

PART A:

In all of this question, let I = [tex]\int ^{2}_{-2} f(x)dx [/tex] [tex]where f(x) = -2x + 1 [/tex]

Evaluate I.

PART B:

Use the defintion of the definite integral to evaluate I.

i.e Riemann Sum.

2. Relevant equations

3. The attempt at a solution

PART A:

I = [-(2)^2 + (2)] - [-(-2)^2 + (-2)]

I = -2 + 6 = 4

Part B is what i am having trouble with.

X_{k}= a + k([tex]\Delta x[/tex])

a = -2

and

[tex]\Delta x[/tex] = b-a/n = 2- (-2)/n = 4/n

so then

X_{k}= -2 + 4k/n

Now the Reimann sum is:

[tex]\sum f(Xk)(\Delta x)[/tex] = [tex]\sum [-2(-2 + 4k/n) + 1](4/n)[/tex]

= 4/n [tex]\sum 4 - 8k/n + 1 [/tex]

= 4/n [tex]\sum -8k/n + 5[/tex]

= 4/n x -8/n [tex]\sum k[/tex] + [tex]\sum 5[/tex]

= -32/n^{2}x [(n)(n+1)/2] + 5n

Now when i take the limit approaching infinity for that, it doesnt give me 4 as an answer unless im doing something wrong.

This is where i am stuck at.

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# Homework Help: Need some help with Riemann Sums.

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