- #1

DemiMike

- 9

- 0

Use the definiton of the definite inegral (with right hand rule) to evaluate the following integral. Show work please

Can NOT use shortcut method.. must be the long process

Function:

1

S (3x^2 - 5x - 6) dx

-4

Work:

∫[-4,1] (3x^2 - 5x - 6) dx =

lim[n-->∞] 5/n ∑[i=1 to n] {3(-4 + 5/n)² - 5(-4 + 5/n) - 6} =

lim[n-->∞] 5*∑[i=1 to n] (48/n - 120i/n² + 75i²/n³ + 20/n -25i/n² - 6/n) =

lim[n-->∞] 5*∑[i=1 to n] (62/n - 145i/n² + 75i²/n³) =

lim[n-->∞] 5[62n/n - 145n(n+1)/(2n²) + 75n(n+1)(2n+1)/(6n³)] =

5(62 - 145/2 + 25) = 72.5

∑[i=1 to n] 1 = n

∑[i=1 to n] i = n(n+1)/2

∑[i=1 to n] i² = n(n+1)(2n+1)/6

Please check if this is correct and let me know