I just have a pretty basic Question.
If your finding the area between two curves, your answer should always be a positive number right?
The reason I am asking is because of this question:
Find the area of the region bounded by y=3x2 & y=9x
The answer I came up with is:
27/2 or 13.5
But when I checked the answer sheet it said the answer is:
-27/2
I was using the Riemanns sum method for finding my answer in case that matters.
I don't want to just automatically assume that you can't have a negative answer to this type of problem so I wanted to ask.
Here's my work the notation isn't that great hopefully its understandable though...
0∫3(9x)dx - 0∫3(3x²)
9 0∫3(x) - 30∫3(x²)
9[(1/2*x²)]30 - [(1/3*x³)]30
9*(1/2*9) - [3*(1/3*27)]
(9*9/2) - (9*3)
81/2 - 27
= 27/12
If your finding the area between two curves, your answer should always be a positive number right?
The reason I am asking is because of this question:
Find the area of the region bounded by y=3x2 & y=9x
The answer I came up with is:
27/2 or 13.5
But when I checked the answer sheet it said the answer is:
-27/2
I was using the Riemanns sum method for finding my answer in case that matters.
I don't want to just automatically assume that you can't have a negative answer to this type of problem so I wanted to ask.
Here's my work the notation isn't that great hopefully its understandable though...
0∫3(9x)dx - 0∫3(3x²)
9 0∫3(x) - 30∫3(x²)
9[(1/2*x²)]30 - [(1/3*x³)]30
9*(1/2*9) - [3*(1/3*27)]
(9*9/2) - (9*3)
81/2 - 27
= 27/12
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