Question

Definition of the definite integral question:

Answer 1

Using the definition of the definite integral, compute:

\[\int\limits_{-4}^{2}(3x^2+12x+20)dx\]

Answer 2

Is the definition of a definition integral FTC or the definition of an integral: lim (x,y)-> (0,0) and on and on?

Answer 3

take the anti derivative of 3x^2 + 12x + 20
is x^3 +6x + 20x then you plug in 2 and then -4
(2)^3 + 6(2) + 20(2) - [ -4^3 + 12(-4) + 20(-4) ]
8 + 12 + 40 - [ -64 - 48 - 80 ]
60 - [ - 192]
= 252

Answer 4

Definition of integral.

@jayz657 Thanks but I want an explanation on this concept.

Answer 5

I can calculate the anti derivative fine but I have to use Riemann sums @jayz657 .

Answer 6

Just an explanation of some sort for Riemann sums would be fine. I can do the rest I am sure.

Answer 7

this is the riemann sum, you are drawing an infinite amount of rectangles under the curve here
you know the length is change of x and the height is f(x) and you sum up each rectangle to get the area under the curve so will will get this

\[\sum_{-4}^{2} f(x)\Delta x\]