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Dido525Best ResponseYou've already chosen the best response.0
Using the definition of the definite integral, compute: \[\int\limits_{4}^{2}(3x^2+12x+20)dx\]
 one year ago

malicalBest ResponseYou've already chosen the best response.0
Is the definition of a definition integral FTC or the definition of an integral: lim (x,y)> (0,0) and on and on?
 one year ago

jayz657Best ResponseYou've already chosen the best response.1
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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Definition of integral. @jayz657 Thanks but I want an explanation on this concept.
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I can calculate the anti derivative fine but I have to use Riemann sums @jayz657 .
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Just an explanation of some sort for Riemann sums would be fine. I can do the rest I am sure.
 one year ago

jayz657Best ResponseYou've already chosen the best response.1
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 \[\sum_{4}^{2} f(x)\Delta x\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Yes I know the fundamental concept. But how would I exactly apply it?
 one year ago

jayz657Best ResponseYou've already chosen the best response.1
when you sum up the infinite amount of rectangles you will get the integral there
 one year ago

malicalBest ResponseYou've already chosen the best response.0
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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Yeah but How would I exactly sum up an infinite number of rectangles for my given function?
 one year ago

malicalBest ResponseYou've already chosen the best response.0
Do you want to see how to do this problem or the theory behind it?
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
@malical : I know how to find an antiderivative. I just have trouble applying riemann sums.
 one year ago

malicalBest ResponseYou've already chosen the best response.0
Why are Riemann sums important?
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
The question specifically says to use Riemann sums.
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Never mind. I got it :) .
 one year ago

jayz657Best ResponseYou've already chosen the best response.1
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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Yeah I got it thanks :) .
 one year ago
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