# Some Form of integral question! who knows

• December 5th 2008, 07:19 AM
Ash_underpar
Some Form of integral question! who knows
Let $F=[2 \sin (x) \cos (x), 0, 2z]$ and $r(t)=[\cos (t),\sin (t),t]$

Calculate $\int_0^{2\pi} F(r(t)).r(t)dt$
• December 6th 2008, 01:17 AM
CaptainBlack
Quote:

Originally Posted by Ash_underpar
Let $F=[2 \sin (x) \cos (x), 0, 2z]$ and $r(t)=[\cos (t),\sin (t),t]$

Calculate $\int_0^{2\pi} F(r(t)).r(t)dt$

I'm not sure your notation makes sense as it is. $F$ is a function of two(?) (real?) variables taking values in $\mathbb(R)^3$, and $r$ is a function of a single (real?) variable taking values in $\mathbb(R)^3$, so $F(r(t))$ is not properly defined. I expect with a bit of effort we could make some sort of guess about what this is supposed to denote but it would be better if you sorted it out.

CB
• December 7th 2008, 06:25 AM
Ash_underpar
Quote:

Originally Posted by CaptainBlack
I'm not sure your notation makes sense as it is. $F$ is a function of two(?) (real?) variables taking values in $\mathbb(R)^3$, and $r$ is a function of a single (real?) variable taking values in $\mathbb(R)^3$, so $F(r(t))$ is not properly defined. I expect with a bit of effort we could make some sort of guess about what this is supposed to denote but it would be better if you sorted it out.

CB

I figured that F(r(t)) could be worked out by using the vector format and taking xi,yj,zk to equal the values of the three points of r(t) taking the y value as 0y, and then integrate the dot product between this value and r(t), which is what i am stuck on but the question i have been set is written exactly as i have put on here.

In textbooks i have used, F seems to be denoted by F(r), but i don't know if thats actually a completely separate value!
{"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": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9496504664421082, "perplexity": 348.42057110318757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "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": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500833461.95/warc/CC-MAIN-20140820021353-00226-ip-10-180-136-8.ec2.internal.warc.gz"}