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.