Question and Answers Forum

All Questions      Topic List

Differentiation Questions

Previous in All Question      Next in All Question      

Previous in Differentiation      Next in Differentiation      

Question Number 173836 by mathlove last updated on 19/Jul/22

Commented by aleks041103 last updated on 21/Jul/22

$$I={\int }_{-2}^{-1}(10\sqrt[4]{x^6}-2x)dx=$$$$=10{\int }_{-2}^{-1}\sqrt[4]{x^6}dx-{\int }_{-2}^{-1}2xdx=$$$$=10J-{\left[x^2\right]}_{-2}^{-1}=16\sqrt{2}-(1-4)=3+16\sqrt{2}$$$$x^{6}iseven\Rightarrow J={\int }_{-2}^{-1}\sqrt[4]{x^6}dx={\int }_1^2\sqrt[4]{x^6}dx={\int }_1^2{x}^{3/2}dx=$$$$={\left[\frac{2}{5}{x}^{5/2}\right]}_1^2=\frac{8\sqrt{2}}{5}$$$$$$

Answered by CElcedricjunior last updated on 19/Jul/22

$$\mathbf{I}={\int }_{-2}^{-1}(10\sqrt{{\mathit{x}}^3}-2\mathit{x})\mathit{d}\mathit{x}={\int }_{-2}^{-1}(10{\mathbf{x}}^{\frac{3}{2}}-2\mathbf{x})\mathbf{dx}$$$$or\sqrt{{\mathbf{x}}^3}{\mathbf{n}}^{\prime }\mathbf{est}\mathbf{definie}\mathbf{en}[-2;-1]$$$$\mathbf{alors}\mathbf{I}{\mathbf{n}}^{\prime }\mathbf{existe}\mathbf{pas}\mathbf{dans}\mathbb{R}$$$$\mathbf{m}\mathit{a}\mathit{i}\mathit{s}\mathit{d}\mathit{a}\mathit{n}\mathit{s}\mathbb{C}$$

Answered by a.lgnaoui last updated on 19/Jul/22

$$$$$$\mathrm{I}=10{\int }_{-2}^{-1}{x}^{\frac{3}{2}}dx-2\int xdx$$$$\mathrm{I}=10{\left[\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}\right]}_{-2}^{-1}-2{\left[\frac{x^2}{2}\right]}_{-2}^{-1}=4{\left[x^2\sqrt{x}\right]}_{-2}^{-1}-{\left[x^2\right]}_{-2}^{+1}$$$$={\left[x^2(4\sqrt{x}-1)\right]}_{-2}^{-1}x<0\Rightarrow \sqrt{x}=\sqrt{\mid x\mid i^2}=i\sqrt{\mid x\mid }$$$$\mathrm{I}={\left[x^2(4i\sqrt{\mid x\mid }-1)\right]}_{-2}^{-1}=4i-1-16\sqrt{2}i+4$$$$\mathrm{I}=3+(4-16\sqrt{2})i=3-18,56i$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com