Definition of the definite integral question:

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

- anonymous

Definition of the definite integral question:

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

Using the definition of the definite integral, compute:
\[\int\limits_{-4}^{2}(3x^2+12x+20)dx\]

- anonymous

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

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

|dw:1353040377471:dw|
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
\[\sum_{-4}^{2} f(x)\Delta x\]

- anonymous

Yes I know the fundamental concept. But how would I exactly apply it?

- anonymous

when you sum up the infinite amount of rectangles you will get the integral there

- anonymous

You integrate the equation and then you get a function. That function will be in terms of f(x). The top number in the definite integral is b and the lower is a. f(b)-f(a) is your answer. Jayz got 252

- anonymous

Yeah but How would I exactly sum up an infinite number of rectangles for my given function?

- anonymous

Do you want to see how to do this problem or the theory behind it?

- anonymous

@malical : I know how to find an antiderivative. I just have trouble applying riemann sums.

- anonymous

Why are Riemann sums important?

- anonymous

The question specifically says to use Riemann sums.

- anonymous

Never mind. I got it :) .

- anonymous

the change of x is the rate of change of each rectangle and rate of change is related to the derivative, dx
so in this equation you can just draw as many rectangles as you want under the curve using a delta x width and using f(x) as your height
heres an exmaple doing it the long way lets say i make 4 rectangles with length 3
|dw:1353040955063:dw|

- anonymous

Yeah I got it thanks :) .

- anonymous

ok np

Looking for something else?

Not the answer you are looking for? Search for more explanations.