Category: Integration

Question Number 207938 by necx122 last updated on 31/May/24 $$whatistheareaboundedbythecurve$$$$y=x(x-2)(x-5)andthexaxis?$$$$$$ Answered by mr W last updated on 31/May/24 $${A}=\int_{\mathrm{0}}…

Question Number 207906 by nachosam last updated on 30/May/24 $$help$$$${\int }_1^{\mathrm{\infty }}{x}^{-ln\left(x\right)}dx$$$$$$ Answered by Berbere last updated on…

Question Number 207857 by necx122 last updated on 28/May/24 $$\int x{\tan }^{-1}xdx$$ Answered by Ghisom last updated on 28/May/24 $$\mathrm{by}\mathrm{parts}$$$$\int x\arctan xdx=$$$$=\frac{{x}^{\mathrm{2}}…

Question Number 207753 by efronzo1 last updated on 25/May/24 Answered by Berbere last updated on 25/May/24 $$A=\underset{k=1}{\sum ^{2023}}\frac{1}{k(k+1)}=\underset{k=1}{\sum ^{2023}}\frac{k+1-k}{k(k+1)}=\underset{k=1}{\sum ^{2023}}\frac{1}{k}-\frac{1}{k+1}$$$$=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2024}}=\frac{\mathrm{2023}}{\mathrm{2024}}…

Question Number 207652 by universe last updated on 22/May/24 $${\int }_0^1\log (1+x^3)dx=?and{\int }_0^1\log (1+x^4)dx=?$$$$\mathrm{and}\mathrm{if}\mathrm{possible}\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{p}$$$$\mathrm{p}={\int }_0^1\log (1+x^n)dx=?n\in \mathbb{N}$$…