Friday

January 30, 2015

January 30, 2015

Posted by **COFFEE** on Tuesday, July 31, 2007 at 1:48pm.

integral from 0 to 1: sin x^2 dx

i'm REALLY stuck on this. and i need help asap..

what is the inverse of "sin x^2" so that i could have it in a fraction that will fit the power series equation? and that is: (A)/(1-R)

You have to use the series expansion of the sin function, not the series expansion of the geometric series.

sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...

So we have:

sin(x^2) = x^2 - x^6/3! + x^10/5! - x^14/7! + ...

Then integrate term by term:

Int sin(x^2) dx =

x^3/3 - x^7/42 + x^11/1320 - x^15/75600 + ...

thank you!!

and to solve to four decimal places... how do i work that? plugging x=0 and x=1?

Yes, you substitute x = 1 and subtract the value you get for x = 0 (but that's zero in this case). The error is of the order of the next term in the series we ignored (you an derive more rigorous error estimates using the Lagrange error formula).

You'll have 6 decimal figures accuracy using the terms up to x^15...

thanks again :)

**Answer this Question**

**Related Questions**

Calculus - 1.evaluate (integral sign)x cos 3x dx A.1/6 x^2 sin 3x + C B.1/3 x ...

Calculus - Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I ...

Calculus - Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I ...

calculus - state the power series of an appropriate familiar function and use it...

Calculus - This is going to be pretty hard to show as text since it would be ...

Calculus - 6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b...

College Calculus (Binomial Series) - Expand f(x) = (x+x^2)/((1-x)^3) as a power ...

Calculus - Taylor #2 - Find the Taylor series for f(x) centered at the given ...

Calculus - a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure...

calculus - With power series, is an endpoint convergent if you plug it back into...