- #1
professordad
- 18
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Please give only hints, no full solutions :)
Use series to approximate the definite integral to within the indicated accuracy:
[itex]\int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}[/itex], [itex]|\text{error}| < 10^{-8}[/itex]
Taylor series and Maclaurin series
This doesn't seem to match or bear resemblance to any of the "famous" ones which can easily be expressed with series [itex]e^x, \sin{x}, \cos{x}[/itex], and I tried taking seven derivatives, but this is awfully annoying. Are there any other methods?
Thanks.
Homework Statement
Use series to approximate the definite integral to within the indicated accuracy:
[itex]\int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}[/itex], [itex]|\text{error}| < 10^{-8}[/itex]
Homework Equations
Taylor series and Maclaurin series
The Attempt at a Solution
This doesn't seem to match or bear resemblance to any of the "famous" ones which can easily be expressed with series [itex]e^x, \sin{x}, \cos{x}[/itex], and I tried taking seven derivatives, but this is awfully annoying. Are there any other methods?
Thanks.
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