Integral and Fundamental Theorem of Calculus

[jkeatin]

Homework Statement

Find 2 \int 0 \ (2-x^2)dx

using def of the definite integral and
using FTC

Homework Equations

The Attempt at a Solution

any help on how to start would be great?

 

[Defennder]

This looks really odd. Do you really mean 2\int 0^{2-x^2} dx?

 

[camilus]

naw.I think he means integral from 0 to 2 of 2-x^2..??

 

[jkeatin]

yeah camilus is right

 

[jkeatin]

am i gettin it close, lim n-->infinity {[8/n^3(i^2)] +4}

 

[camilus]

the answer is 4/3.

integral from 0 to 2 of 2-x^2 = [2x-(x^3)/3] evaluated at 2. You can ignore the zero.

2(2)-(2^3)/3 = 4 - 8/3 = (12 - 8)/3 = 4/3

 

[jkeatin]

oh i get ya, and using ftc id get the same answer just a different way correct?

 

[jkeatin]

thanks for the help camilus