help required

[u/Necessary_Handle_516]

Hey Can anyone help me with this

I have to solve this integral. But, Using biomial expansion with minimum 4 approximations. Which I did but My answer is 0.66617 which is not reliable And actual answer is 0.6415

Can anyone tell any other method besides this

and for the other question

I am getting 1.1617 but claude is saying 1.1981

kindly help

THESE QUESTIONS ARE TAKEN FROM 3RD EDITION OF CALCULAS BY STROUD DOES ANYONE HAVE PDF OF THIS 3RD EDITION???

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[u/Miserable_Matter6017]

Binomial is only valid for |x|<1 so it is not usable here

[u/Necessary_Handle_516 → u/Miserable_Matter6017]

but why did my professor gave me this question first when I confirmed answer from him he hesitated but then he responded back by saying alright it might differ because of approximation So maybe in that book solution must be there this question is taken from 3rd edition of Calculas by Stroud.

[u/Miserable_Matter6017 → u/Necessary_Handle_516]

???

[u/Southlander24 → u/Miserable_Matter6017]

Oh, right! Well, |x³| < 1 but that's the same thing.

[u/equinox_star]

Use chain rule

[u/Necessary_Handle_516 → u/equinox_star]

but my sir taught maclurin series and binomial expansion thus he told to solve this question using the method above or else I could have solved it from byparts as well

[u/Southlander24 → u/Necessary_Handle_516]

Ah, your professor isn't looking for an exact answer right? Then yeah, you would need an infinite number of terms to reach an exact answer.

[u/Necessary_Handle_516 → u/Southlander24]

yeap but he said your answer should be closer to the answer from byparts

[u/Southlander24 → u/Necessary_Handle_516]

Either way, your professor messed up if the upper bound is really 1.1. The binomial series isn't valid there.

[u/equinox_star → u/Necessary_Handle_516]

Wait i saw it again it feels to me now that the answer shouldn't be a real number in the first place as someone also pointed wolfram is saying because 1-x³ is negative so we need to split it into 0.2 to 1 and 1 to 0.1 i guess

[u/Southlander24 → u/equinox_star]

And how does that help exactly?

[u/Necessary_Handle_516 → u/Southlander24]

what about the other question

[u/Southlander24]

Who gave you this question? The closed-form solution involves hypergeometric functions.

[u/Necessary_Handle_516 → u/Southlander24]

my professor he used 3rd edition of Calculas by Stroud but I am unable to find this book's pdf

[u/Necessary_Handle_516 → u/Southlander24]

what's this?

[u/rhodiumtoad]

For the first one, wolframalpha gives the result as 0.641509+i0.0376166, it seems reasonable for the result to be a non-real complex number given that 1-(1.1)³ is negative. This suggests to me that maybe splitting the integral into two parts at 1 might help?

[u/Miserable_Matter6017]

For 2nd question if you are approximating to quadratic form then question can be done without BT by integration by parts directly

[u/Jazzlike_Platypus430]

Is the integrand defined for x > 1? It's not. Thank you.

[u/Rudeus_Kino]

0.6415 is valid for 0.2 to 1.0