# calculus - power series ASAP please :)

using power series, integrate & evaluate to 4 dec. places

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 :)

1. 👍 0
2. 👎 0
3. 👁 197

## Similar Questions

1. ### Maths

Question : Integrate [x/(1+(sin a*sin x))] from 0 to pi My first thought was to apply integrate f(x) dx= f(a-x) dx method Which simplified the integral into; 2I = integrate [pi/(1+(sin a*sin x))] dx , cancelling out x Then I made

asked by Ashley on March 18, 2019
2. ### Math/Calculus

How would I integrate the following by parts: Integral of: (x^2)(sin (ax))dx, where a is any constant. Just like you did x^2 exp(x) below. Also partial integration is not the easiest way to do this integral. You can also use this

asked by COFFEE on May 28, 2007
3. ### Calculus

1.evaluate (integral sign)x cos 3x dx A.1/6 x^2 sin 3x + C B.1/3 x sin 3x -1/2 sin 3x +C C.1/3 x sin 3x +1/9 cos 3x +C

asked by anon on March 12, 2011
4. ### Calculus

The prompt for all of these question is "consider the function f(x) = sin^2(x)". Part A: Write the first four terms of the Maclaurin series for f(x). I assumed this implied non-zero terms, so I found

asked by Amanda on June 2, 2017
5. ### Math

The prompt for this question is f(x) =sin(x^2) A)Write the first four terms of the Maclaurin series for f(x) B)Use the Maclaurin series found in Part A to approximate the integral from 0 to 1 of sin(x^2) dx C)How many terms are

asked by Anon on February 4, 2018
6. ### Math

The prompt for this question is f(x) =sin(x^2) A)A. Write the first four terms of the Maclaurin series for f(x) B)Use the Maclaurin series found in Part A to approximate the integral from 0 to 1 of sin(x^2) dx C)C. How many terms

asked by Anon on February 3, 2018
7. ### Math (Calculus)

The prompt for this question is f(x) =sin(x^2) A)Write the first four terms of the Maclaurin series for f(x) B)Use the Maclaurin series found in Part A to approximate the integral from 0 to 1 of sin(x^2) dx C)How many terms are

asked by Anon on February 4, 2018
8. ### trig integration

s- integral endpoints are 0 and pi/2 i need to find the integral of sin^2 (2x) dx. i know that the answer is pi/4, but im not sure how to get to it. i know: s sin^2(2x)dx= 1/2 [1-cos (4x)] dx, but then i'm confused. The indefinite

asked by christine on February 18, 2007
9. ### Integral calculus

Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these

asked by Febby on April 13, 2007
10. ### Calculus II/III

A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of

asked by Ryoma on February 19, 2007

More Similar Questions