Question Number 183073 by Mastermind last updated on 19/Dec/22
$$\int\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Integrate}\:\mathrm{this}\:\mathrm{question} \\ $$
Answered by Ml last updated on 20/Dec/22
$$\int\mathrm{sin}^{\mathrm{2}} \mathrm{xdx}=? \\ $$$$\mathrm{note}\therefore\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}=\frac{\mathrm{1}−\mathrm{cos2x}}{\mathrm{2}} \\ $$$$\int\frac{\mathrm{1}−\mathrm{cos2x}}{\mathrm{2}}\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}}\int\left(\mathrm{1}−\mathrm{cos2x}\right)\mathrm{dx} \\ $$$$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin2x}+\mathrm{C}\:\:\:,\:\mathrm{C}\in\mathbb{R} \\ $$$$\mathrm{Eng}−\bigstar \\ $$
Commented by Mastermind last updated on 19/Dec/22
$$\mathrm{That}'\mathrm{s}\:\mathrm{good},\:\mathrm{you}\:\mathrm{got}\:\mathrm{it}\:\mathrm{correct}! \\ $$
Answered by BaliramKumar last updated on 20/Dec/22
$$\int{sin}^{\mathrm{2}} {xdx} \\ $$$$\int\sqrt{{sin}^{\mathrm{2}} {x}}\centerdot{sinxdx} \\ $$$$\int\sqrt{\mathrm{1}−{cos}^{\mathrm{2}} {x}}\centerdot{sinxdx} \\ $$$${let}\:\:\:{cosx}\:=\:{t}\:\:\:\:\:\:\:\:\:−{sinxdx}\:=\:{dt} \\ $$$$−\int\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }{dt} \\ $$$$………. \\ $$