- #1
nameVoid
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Mastering the Definite Integral: A Comprehensive Guide
- Thread starter nameVoid
- Start date
- #2
CompuChip
Science Advisor
Homework Helper
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Welcome to PF nameVoid.
Let's start by finding an anti-derivative (primitive)... you need something which will give you
\sqrt{x - 2} = (x - 2)^{1/2}
when you differentiate it... can you make a wild guess?
Let's start by finding an anti-derivative (primitive)... you need something which will give you
\sqrt{x - 2} = (x - 2)^{1/2}
when you differentiate it... can you make a wild guess?
- #3
nameVoid
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using the definition
im not clear on how to expand the expression to distribute the sum
im not clear on how to expand the expression to distribute the sum
- #4
Mark44
Mentor
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Look at CompuChip's post again. He's not asking you to use the definition of the definite integral, but rather asking you if you can think of a function whose derivative is sqrt(x - 2).
IOW, d/dx(____) = (x - 2)^(1/2).
Can you fill in the blank?
IOW, d/dx(____) = (x - 2)^(1/2).
Can you fill in the blank?
- #5
NoMoreExams
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Why don't you just do a subst. u = x - 2?
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Hello,
This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread.
Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).
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