Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 209659 by mokys last updated on 17/Jul/24

Answered by efronzo1 last updated on 18/Jul/24

$$\mathrm{S}=\underset{0}{\stackrel{1}{\int }}{2}^{\mathrm{x}}\mathrm{dx}+\underset{1}{\stackrel{\sqrt{3}}{\int }}(3-{\mathrm{x}}^2)\mathrm{dx}$$

Answered by mr W last updated on 18/Jul/24

Commented by mr W last updated on 18/Jul/24

$$T={\int }_0^1(3-x^2-2^x)dx$$$$={[3x-\frac{x^3}{3}-\frac{2^x}{\ln 2}]}_0^1$$$$=3-\frac{1}{3}-\frac{2-1}{\ln 2}=\frac{8}{3}-\frac{1}{\ln 2}$$$$S+T=\frac{2}{3}\times 3\times \sqrt{3}=2\sqrt{3}$$$$\Rightarrow S=2\sqrt{3}-\frac{8}{3}+\frac{1}{\ln 2}\approx 2.24$$

Answered by lepuissantcedricjunior last updated on 18/Jul/24

$$\mathit{f}\left(\mathit{x}\right)=3-{\mathit{x}}^2;\mathit{g}\left(\mathit{x}\right)=2^{\mathit{x}}$$$$2^{\mathit{x}}+{\mathit{x}}^2-3=0=>\mathit{x}=1=>0⩽\mathit{x}⩽1$$$$\mathit{S}={\int }_0^1{\int }_0^{2^{\mathit{x}}}\mathit{d}\mathit{x}={\left[\frac{1}{\mathit{l}\mathit{n}2}{2}^{\mathit{x}}\right]}_0^1=\frac{1}{\mathit{l}\mathit{n}2}\approx \frac{1}{0.69}\approx \frac{100}{69}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com