- #1
Dorothy Weglend
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- 2
Homework Statement
By appealing to geometric evidence show that
[tex]\int_0^8x^n\,dx + \int_0^1 x^{1/n}\,dx = 1[/tex]
for n a positive integer.
Homework Equations
Fundamental theorem of calculus, power rule for integration.
The Attempt at a Solution
I integrated. For the first integral, I get:
[tex] \frac{8^{n+1}}{n+1}[/tex]
and for the second:
[tex] \frac{n}{n+1} [/tex]
As an experiment, I tried this for a few values of n, for example, n=1 gives [itex] 8^2/2 + 1/2 = 32.5 [/tex], which is certainly not 1.
So obviously something is awry here. I think I integrated properly, but perhaps not.
Can someone shed some light on this for me?
Thank you,
Dorothy
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