Can someone help me with this problem? Evaluate the integral of sin(x^3) from 0 to 1 as a sum of fractions with an error of at most 10^-3. Identify the minimum number of terms required to achieve this accuracy.

Question

logando · Answer

$$\int\limits_{0}^{1} \sin(x^{3})dx$$

ijlal · Answer

are you familiar with gamma integrals? @LoganDo

ijlal · Answer

and Euler identities as well

logando · Answer

I'm not sure. I don't recognize the terms. All I know is that the problem has something to do with series, so I thought that maybe I would use the error for alternating series?

ijlal · Answer

are u sure it aint $$\int\limits_{0}^{1 }\sin^3x$$? cause the i worked out your integral it seems a bit messy

ijlal · Answer

http://www.integral-calculator.com/ use this site to help yourself to calculate it's integral

logando · Answer

It's definitely sin(x^3).

logando · Answer

I'm pretty sure it's just using the power series for sin(x) and replacing x with x^3, but I just don't know how to find the error at most 10^-3

ijlal · Answer

it's mixup of gamma functions using Euler identities as substitution and basic gamma formula for the integral

logando · Answer

That's not the point of the problem though. It's not asking for you to just evaluate the integral. It wants you to evaluate it "as a sum of fractions" with an error of at most 10^-3

ijlal · Answer

sorry i'll see myself out of this one cant help you with this i know someone who might tagging him

logando · Answer

LOLOL it's fine, man. It's a weird one. My professor's a bit tricky. Thanks for trying though!

ijlal · Answer

@TheSmartOne  @ganeshie8  @ParthKohli

welshfella · Answer

lets look what wolfram gives.

welshfella · Answer

https://www.wolframalpha.com/input/?i=Integrate++sin+(x%5E3) thats gives it in a few different forms.

welshfella · Answer

I guess you could write it as a Taylor series  but its been  a long time.....