- #1
imjustcurious
- 21
- 0
Originally posted in a non-homework section, so missing the template
In one of the homework sheets my teacher gave us, we had to calculate area geometrically (meaning no integration was used). Some parts, she said, we needed to just eyeball which I hate doing. In this case the top left portion of a circle described by the equation...
https://lh4.googleusercontent.com/RksM0NW9ZgHNhfNFiZk6LZScXMRRTw9bIc76W9q8udnF4Qy48n4HmG5f526lezK8bEMipFLHJvp-hPN97gcSZYtb6ix0O9TQxnrV6IXAG7VGMPdtkASNYGxDtZgOvIsrc0gHHqa4
was shown and we need to find the area from [6,8]. So I integrated the equation from 6 to 8 with respect to x...
https://lh5.googleusercontent.com/JVPHXihl_rTOFyRbQMGlATw5i1spj0qU4c5taOghVF_q7f-jyI4VTvtBeK69XOI76hnqw2FhdUt5Vzayfa-cBZ1iCC7Fhw5RKsOFo6OxlPBndtCLk-gvFrNwR4Z3KaVlS00t7Jxk
https://lh6.googleusercontent.com/QI58405jGPaitde0HrZfC_zJrsB4iEoixqs9AkqV8eyr4dCLYeSd64WccercpncO3bElIcfRd_HJttVC8hnMpmX9aZJJYwhpBXlO1Y5WYI99wubqFDl5bErVTOaxZUs9vSOLLmQo
I am not sure how to integrate this by hand so I used Mathway.com and it spit out this.
https://lh4.googleusercontent.com/hVf_R-YZA8zDWUU3Sm-0lQt8SpkIiVlJy-JXYCBMrYwiBlx_jzuUOUwn7dJjxaVRv5JxYQ1aO2TQl6i94iGe_Fri_CgcP-y6kO2xuKJvvgWmQUISoAN7JGEpSVDCJX47VX_2P5s8
I don't completely understand what this means. I graphed it to find where the zeros are and got
https://lh6.googleusercontent.com/El282NKbIJn3H7_uPivwQaP_VqX0WPFllVwqKbn5R7FO3u4_-yI_TgeoJLoiwx7nFBHFo901-kxUEkAOQufVZE8Ku4q078oa29X3lmDPZjXndfpNEz97JuWPQPa-AFhbL9pFfvb3
At first it looked to me as though the negative number is the area under the x-axis from 6 to 8 and the positive number is the area above the x-axis from 6 to 8. However, when I do eyeball it, it looks like those values should be doubled which is what causes my confusion. If anyone can explain any flaws in my math or what this means, I would appreciate it. Thanks.
https://lh4.googleusercontent.com/RksM0NW9ZgHNhfNFiZk6LZScXMRRTw9bIc76W9q8udnF4Qy48n4HmG5f526lezK8bEMipFLHJvp-hPN97gcSZYtb6ix0O9TQxnrV6IXAG7VGMPdtkASNYGxDtZgOvIsrc0gHHqa4
was shown and we need to find the area from [6,8]. So I integrated the equation from 6 to 8 with respect to x...
https://lh5.googleusercontent.com/JVPHXihl_rTOFyRbQMGlATw5i1spj0qU4c5taOghVF_q7f-jyI4VTvtBeK69XOI76hnqw2FhdUt5Vzayfa-cBZ1iCC7Fhw5RKsOFo6OxlPBndtCLk-gvFrNwR4Z3KaVlS00t7Jxk
https://lh6.googleusercontent.com/QI58405jGPaitde0HrZfC_zJrsB4iEoixqs9AkqV8eyr4dCLYeSd64WccercpncO3bElIcfRd_HJttVC8hnMpmX9aZJJYwhpBXlO1Y5WYI99wubqFDl5bErVTOaxZUs9vSOLLmQo
I am not sure how to integrate this by hand so I used Mathway.com and it spit out this.
https://lh4.googleusercontent.com/hVf_R-YZA8zDWUU3Sm-0lQt8SpkIiVlJy-JXYCBMrYwiBlx_jzuUOUwn7dJjxaVRv5JxYQ1aO2TQl6i94iGe_Fri_CgcP-y6kO2xuKJvvgWmQUISoAN7JGEpSVDCJX47VX_2P5s8
I don't completely understand what this means. I graphed it to find where the zeros are and got
https://lh6.googleusercontent.com/El282NKbIJn3H7_uPivwQaP_VqX0WPFllVwqKbn5R7FO3u4_-yI_TgeoJLoiwx7nFBHFo901-kxUEkAOQufVZE8Ku4q078oa29X3lmDPZjXndfpNEz97JuWPQPa-AFhbL9pFfvb3
At first it looked to me as though the negative number is the area under the x-axis from 6 to 8 and the positive number is the area above the x-axis from 6 to 8. However, when I do eyeball it, it looks like those values should be doubled which is what causes my confusion. If anyone can explain any flaws in my math or what this means, I would appreciate it. Thanks.