Category: Integration

Question Number 205590 by Lindemann last updated on 25/Mar/24 $$J={\int }_0^1\sqrt{1-x^4}dx$$ Commented by lepuissantcedricjunior last updated on 25/Mar/24 $$\boldsymbol{{J}}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}}…

Question Number 205506 by Lindemann last updated on 23/Mar/24 $${\int }_0^1\sqrt{1-x^4}dx$$ Answered by sniper237 last updated on 23/Mar/24 $$\overset{{u}={x}^{\mathrm{4}} } {=}\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}}…

Question Number 205335 by Lindemann last updated on 17/Mar/24 $$\int \frac{ax+b}{{(x^2-cx+d)}^n}dx$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 205294 by depressiveshrek last updated on 15/Mar/24 $$\int \sqrt[3]{3x-x^3}dx$$ Answered by Frix last updated on 15/Mar/24 $$\int\left(\mathrm{3}{x}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx}\:\overset{{t}=\frac{{x}^{\mathrm{2}} }{\mathrm{3}}} {=}\:\frac{\mathrm{3}}{\mathrm{2}}\int{t}^{−\frac{\mathrm{1}}{\mathrm{3}}}…

Question Number 205315 by cherokeesay last updated on 15/Mar/24 Answered by MM42 last updated on 16/Mar/24 $$\left[x\right]+[x-\frac{1}{2}]=\left[2x\right]-1$$$$\Rightarrow {\int }_0^{\left[x\right]}(\left[2x\right]-1)dx=(\left[2x\right]-1)x{\mid }_0^{\left[x\right]}$$$$=\left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right)\left[{x}\right] \…