Exercise:
Berechne den Schwerpunkt sscxs sscys des folg abgebildeten Kreisabschnittes in Abhängigkeit von delta. center tikzpicturescale. drawcolorgreen!!black -latex -.--. noderight x; drawcolorgreen!!black -latex -.--. nodeabove y; drawcolorblue - arc::; drawcolorgreen!!black dashed -..---.-. nodebelow -delta; drawcolorgreen!!black dashed ..--.-. nodebelow delta; filldrawfillred!!white opacity. -.. arc:: -- cycle; tikzpicture center

Solution:
M rho _V ddV rho _x _y _z ddxddyddz rho _-delta^delta ddx _sqrt-delta^^sqrt-x^ ddy _^d ddz rho d _-delta^delta ddx _sqrt-delta^^sqrt-x^ ddy rho d _-delta^delta ddx y_sqrt-delta^^sqrt-x^ rho d _-delta^delta leftsqrt-x^ - sqrt-delta^ rightddx rho d _-delta^delta leftsqrt-x^ - sqrt-delta^ rightddx rho d _-delta^delta sqrt-x^ddx - rho d _-delta^deltasqrt-delta^ ddx rho d _-delta^delta sqrt-x^ddx - rho d sqrt-delta^ x_-delta^delta rho d _-delta^delta sqrt-x^ddx - delta rho d sqrt-delta^ rho d leftfracleftxsqrt-x^+arcsin xrightright_-delta^delta - delta rho d sqrt-delta^ rho d deltasqrt-delta^+arcsindelta - delta rho d sqrt-delta^ rho d arcsindelta - rho d delta sqrt-delta^ rho d leftarcsindelta - delta sqrt-delta^right Die Schwerpunktskoordinate ist somit: sscys fracM _M y ddm fracM _V y rho ddV fracrhoM _x _y _z y ddxddyddz fracrhoM _-delta^delta _sqrt-delta^^sqrt-x^ _^d y ddxddyddz fracrhoM _-delta^delta ddx _sqrt-delta^^sqrt-x^ y ddy _^d ddz fracrho dM _-delta^delta ddx _sqrt-delta^^sqrt-x^ y ddy fracrho dM _-delta^delta ddx leftfrac y^right_sqrt-delta^^sqrt-x^ fracrho dM _-delta^delta ddx leftfrac -x^-frac-delta^right fracrho dM _-delta^delta fracleftdelta^-x^right ddx fracrho dM frac leftdelta^x-fracx^right_-delta^delta fracrho dM frac delta^ fracrho drho d leftarcsindelta - delta sqrt-delta^right frac delta^ frac fracdelta^arcsindelta - delta sqrt-delta^right