Question Number 154194 by chinomso last updated on 15/Sep/21
Commented by alisiao last updated on 15/Sep/21
$$\int_{\mathrm{9}} ^{\:\mathrm{11}} \:\frac{\boldsymbol{{y}}+\mathrm{8}}{\boldsymbol{{c}}}\:\boldsymbol{{dy}}\:=\:\mathrm{1}\:\Rightarrow\:\frac{\mathrm{1}}{\boldsymbol{{c}}}\:\int_{\mathrm{9}} ^{\:\mathrm{11}} \:\left(\boldsymbol{{y}}+\mathrm{8}\right)\boldsymbol{{dy}}\:=\mathrm{1} \\ $$$$ \\ $$$$\boldsymbol{{c}}\:=\:\left(\frac{\boldsymbol{{y}}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{8}\boldsymbol{{y}}\underset{\:\mathrm{9}} {\right)}^{\mathrm{11}} \:\Rightarrow\:\boldsymbol{{c}}\:=\:\left(\frac{\mathrm{121}}{\mathrm{2}}+\mathrm{88}\right)−\left(\frac{\mathrm{81}}{\mathrm{2}}+\mathrm{72}\right) \\ $$$$ \\ $$$$\boldsymbol{{c}}\:=\:\left(\frac{\mathrm{121}−\mathrm{81}}{\mathrm{2}}\:+\:\mathrm{88}\:−\:\mathrm{72}\right)\:=\:\left(\mathrm{20}\:+\:\mathrm{16}\:\right)\:=\:\mathrm{36}\: \\ $$$$ \\ $$$$\langle\:\boldsymbol{{M}}\:.\:\boldsymbol{{T}}\:\:\rangle \\ $$