Question

Determine the x-coordinate of the centroid of the shaded area. 1 bi - - - 1

Answer 1

Solution Wale will find area of quarter of ellips and then minus the triangle Area of ellips Trab For quarters Area = tlab 4 Ř centroid of ellips = 99 STI Area of thiangle =Laxb 2 ał centroid of triangle C. 3 -X 4 2 3 2 alb T= Tabx 40 xqx bx. 31 Tab lxaxb 4 a²b 3 6 -ablt 2 (TE) I= 4a. 3.61-2) 8 a 6 6 (11-2)

Integration method Tafada SIA Letofind id 20 I102-2)-2x+b)] da a of (bx bx 122x² + bx² bx) dx bx fa²x² dx + b bx2-b27d. a -b367412-x2)€22]dx + bx3_bx2 29 30 2 Jo b f (a²-x2) 312 ba² - ba² 3a 20 2 Le baz 6 - baz 6

(da - Пар Ixaxb 2. .: x- ba? 6 ab() — БЯ GСТІ –2) x = La 5 СТ-21)
I have solved it by standard formula as well as Integration method .