Question

the intergral

(10

4 (2x^2+3x+1)dx

i have to find the sum of the intergral using right and left endpts when n=3. I am confused on how to even start this or how to use these endpts.

Answer 1

What do you mean by the sum of the integral? Do you mean the value of the integral? Are the limits of integration 4 to 10? What is n? It does not appear in the mathematial expression you have written. Are you supposed to be doing a Simpson's Rule numerical integration with n=3 terms?

That is what I assume they want you to do.

The exact value of the integral is
(2/3)x^3 + (3/2)x^2 +x evaluated at x=10, minus the value at x = 4. This is
826.67 - 70.67 = 756

Using Simpson's rule with 3 terms and h=3 as the interval width, I get
(h/3)[f(4) + 4 f(7) + f(10)]
= 1*[45 + 480 + 231) = 756

The agreement is perfect because the curve is a parabola, and Simposn's rule provides a parabolic best fit to each interval.

Answer 2

Find the Riemann sum for this integral using right and left endpoints and n=3. when i type in 756 it shows to be the wrong answer.

Answer 3

You left out the word Riemann before; so I solved the wrong problem.

The Riemann sum is defined here:
http://en.wikipedia.org/wiki/Riemann_integral
It is a less accurate approxiation to the integral than Simpson's rule. I will leave you to calculate it.