Category: Integration

Question Number 215775 by ajfour last updated on 17/Jan/25 $$\underset{0}{\stackrel{s}{\int }}\sqrt{1-s^2}(1+\sqrt{1-{\left(\frac{x}{s}\right)}^2}-\sqrt{1-x^2})dx$$ Commented by ajfour last updated on 18/Jan/25 https://youtu.be/ZcHJ_FnQ6Fk?si=r5hLYfUC_lLg_ccq…

Question Number 215740 by universe last updated on 16/Jan/25 $$$$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}}…

Question Number 215704 by universe last updated on 15/Jan/25 Commented by universe last updated on 16/Jan/25 $$HIMRWpleasesolvethisproblem$$ Answered by mr W last updated…

Question Number 215550 by MrGaster last updated on 10/Jan/25 $$\boldsymbol{\mathrm{Let}}\:\boldsymbol{{u}}^{\left(\mathrm{1}\right)} ,\boldsymbol{{u}}^{\left(\mathrm{2}\right)} \boldsymbol{\mathrm{s}}.\boldsymbol{\mathrm{t}}.\begin{cases}{\boldsymbol{{u}}_{\boldsymbol{{tt}}} ^{\left(\mathrm{1}\right)} =\left(\frac{\partial^{\mathrm{2}} }{\partial\boldsymbol{{x}}_{\mathrm{1}} ^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} }{\partial\boldsymbol{{x}}_{{i}} ^{\mathrm{2}} }\right)\boldsymbol{{u}}^{\left(\mathrm{1}\right)} }\{\boldsymbol{{u}}^{\left(\mathrm{1}\right)} \left(\boldsymbol{{x}}_{\mathrm{1}} ,\boldsymbol{{x}}_{\mathrm{2}} ,\mathrm{0}\right)=\boldsymbol{\psi}\left(\boldsymbol{{x}}_{\mathrm{1}} ,\boldsymbol{{x}}_{\mathrm{2}}…

Question Number 215535 by MrGaster last updated on 10/Jan/25 $${\int }_{\sum _{1\le i\le n}{x}_i^2\le R^2}\sum _{1\le i\le n}{x}_i\frac{\partial f}{\partial x_i}\prod _{1\le i\le n}{dx}_i=?$$ Answered by MrGaster…