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Dido525
 3 years ago
Definition of the definite integral question:
Dido525
 3 years ago
Definition of the definite integral question:

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Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Using the definition of the definite integral, compute: \[\int\limits_{4}^{2}(3x^2+12x+20)dx\]

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

jayz657
 3 years ago
Best ResponseYou've already chosen the best response.1take 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

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Definition of integral. @jayz657 Thanks but I want an explanation on this concept.

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0I can calculate the anti derivative fine but I have to use Riemann sums @jayz657 .

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Just an explanation of some sort for Riemann sums would be fine. I can do the rest I am sure.

jayz657
 3 years ago
Best ResponseYou've already chosen the best response.1dw: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 \[\sum_{4}^{2} f(x)\Delta x\]

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Yes I know the fundamental concept. But how would I exactly apply it?

jayz657
 3 years ago
Best ResponseYou've already chosen the best response.1when you sum up the infinite amount of rectangles you will get the integral there

malical
 3 years ago
Best ResponseYou've already chosen the best response.0You 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

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah but How would I exactly sum up an infinite number of rectangles for my given function?

malical
 3 years ago
Best ResponseYou've already chosen the best response.0Do you want to see how to do this problem or the theory behind it?

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0@malical : I know how to find an antiderivative. I just have trouble applying riemann sums.

malical
 3 years ago
Best ResponseYou've already chosen the best response.0Why are Riemann sums important?

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0The question specifically says to use Riemann sums.

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Never mind. I got it :) .

jayz657
 3 years ago
Best ResponseYou've already chosen the best response.1the 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

Dido525
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah I got it thanks :) .
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