# Thread:

1. ## Integral Area

Hello fellow math members!

I can't find this area of this two function intersecion:
Y1= $x^3-x$
Y2=sin(pi*x)

For $-1\leq x\leq 1$

From what I know, I need to do y1=y2 initially, right?
But even that I did't get to resolve =/

Any help? ^^

Here is the answer:
Spoiler:
Area=(8+pi)/pi

Thanks!

2. ## Re: Integral Area

A graphical representation of the intersections of the two functions would be sufficient in my opinion, but if you want to be slightly more rigorous:

When x = -1, 0, 1 then both $x^3-x = x(x-1)(x+1)$ and $sin([pi x)$ = 0
In the interval (-1,0), $sin([pi x) > 0$ and $x^3-x < 0$ so the two functions cannot be equal.
In the interval (0,1), "" < 0 and "" > 0 so the two functions cannot be equal.

Hence the only intersection points are -1, 0, 1. then set up your integrals.

one will be from -1 to 0 with $sin(pi x) - (x^3-x)$ and the other will be from 0 to 1 with $(x^3-x) - sin(pi x)$. After solving both, add them to get your total area.

3. ## Re: Integral Area

Thanks a lot mate!
Just did it!
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8863198161125183, "perplexity_flag": "middle"}