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Evaluate this definite integral 20x + 3x^2  (2/3)x^3 from [2, 5] ? 
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#1
Jun1610, 02:05 PM

P: 165

1. The problem statement, all variables and given/known data
I get the answer 19/3 but the real answer is 343/3. Can you show work to how it is that? I did this many times and still came up with 19/3 instead I got up to evaluating the integral part of finding the area between two curves but can never get the correct answer. I have a feeling I'm messing up signs somewhere. 


#2
Jun1610, 02:19 PM

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Are you sure you copied the problem correctly? I don't get either of your answers. It would be helpful for you to show what you did.



#3
Jun1610, 05:44 PM

P: 165

Yeah.
Let f(x) = 20 + X + X^{2} Let g(x) = X^{2}5X Find the area of the region enclosed by the two graphs. The graphs intersect at X = 2 and 5, so those are the bounds. F(x) is the upper curve. So I take the definite integral of [(20 + X  X^2)  (X^25X)dx] from [2, 5] The answer is 343/3, but I do not get that answer when I compute the integral at all 


#4
Jun1610, 06:27 PM

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Evaluate this definite integral 20x + 3x^2  (2/3)x^3 from [2, 5] ?
f(2) = 20 2 + 4 = 22 g(2) = 4 + 10 = 14 f(5) = 20 + 5 + 25 = 50 g(5) = 25  25 = 0 If you set 20 + x + x^{2} = x^{2}  5x, notice that you can subtract x^{2} from both sides, leaving you with a linear equation  an equation that has only one solution. I don't see that the two graphs enclose any region, so I don't know how you can do this problem. Are you sure you have all the information straight? 


#5
Jun1610, 06:34 PM

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If you post the actual problem statement, exactly as it is written, that would be a big help. 


#6
Jun1610, 06:59 PM

P: 165

The problem in my Calc book just stated
Let f(x) = 20 + X  X^2 Let g(x) = X^25X Find the area of the region enclosed by the two graphs. I set these two equal to each other 20 + X + X^2 = X^25X Through Algebra, I found that 0 = 2X^2  6X 20 which factors to 2(X5)(X+2) Thus the curves intersect at X = 2 and X = 5. I made a mistake earlier saying that the graphs intersected at those two points; sorry. f(x) is the upper curve. From there they just used used the formula for calculating the area between curves and obtained the answer 343/3 but i cannot work out the math to get that 


#7
Jun1610, 07:39 PM

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#8
Jun1610, 08:05 PM

P: 165

Aw damn, now I know why. Good catch. I wrote the equation for f(x) incorrectly. It was supposed to be
20 + X  X^2 not 2+ + X + X^2 Now what I wrote before makes sense 


#9
Jun1710, 06:11 AM

P: 317




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