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Category: Integration

Find-the-volume-of-the-region-bounded-by-the-elliptic-paraboloid-z-4-x-2-1-4-y-2-and-the-plane-z-0-

Question Number 144528 by imjagoll last updated on 26/Jun/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\: \\ $$$$\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{elliptic}\:\mathrm{paraboloid} \\ $$$$\mathrm{z}\:=\:\mathrm{4}−\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\mathrm{y}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{z}=\mathrm{0} \\ $$$$ \\ $$ Answered by EDWIN88 last updated…

Calculus-I-P-0-pi-2-xcos-x-1-e-sin-x-dx-0-pi-2-xsin-x-1-e-cos-x-dx-

Question Number 144527 by mnjuly1970 last updated on 26/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:…..\:\:\:\mathrm{Calculus}\:\:\left(\mathrm{I}\:\right)….. \\ $$$$\mathrm{P}:=\:\frac{\int_{\mathrm{0}\:} ^{\:\:\frac{\pi}{\mathrm{2}}} \left(\:{xcos}\left({x}\right)+\mathrm{1}\:\right){e}^{\:{sin}\left({x}\right)} {dx}\:}{\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\:{xsin}\left({x}\right)\:−\mathrm{1}\:\right){e}^{\:{cos}\left({x}\:\right)} {dx}}=? \\ $$ Answered by Kamel…

Calculus-I-Lim-x-0-1-cos-xcos-x-2-cos-x-4-cos-x-8-x-2-

Question Number 144450 by mnjuly1970 last updated on 25/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:………\mathrm{C}{alculus}\left(\mathrm{I}\right)……… \\ $$$$\:\:\mathrm{Lim}_{\:\:{x}\:\rightarrow\:\mathrm{0}} \frac{\mathrm{1}\:−{cos}\left({xcos}\left(\frac{{x}}{\mathrm{2}}\right).{cos}\left(\frac{{x}}{\mathrm{4}}\right){cos}\left(\frac{{x}}{\mathrm{8}}\right)\right)}{{x}^{\:\mathrm{2}} }=? \\ $$ Answered by Dwaipayan Shikari last updated on…

0-3-3-2-x-3-4x-2-9-dx-

Question Number 13364 by tawa tawa last updated on 19/May/17 $$\int_{\:\:\:\mathrm{0}} ^{\:\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}} \:\:\:\frac{\mathrm{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{4x}^{\mathrm{2}} \:−\:\mathrm{9}}}\:\:\mathrm{dx} \\ $$ Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 19/May/17 $${you}\:{should}\:{change}\:{the}\:{limits}\:{of}\:{integral}.…

x-3-16-x-2-dx-

Question Number 13362 by tawa tawa last updated on 19/May/17 $$\int\:\frac{\mathrm{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{16}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 19/May/17 $${I}=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{{x}^{\mathrm{2}} \left(\mathrm{2}{xdx}\right)}{\:\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }}…

x-3-2x-x-2-dx-

Question Number 13360 by tawa tawa last updated on 19/May/17 $$\int\:\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{3}\:−\:\mathrm{2x}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx} \\ $$ Answered by ajfour last updated on 19/May/17 $$\boldsymbol{{I}}=\int\frac{\mathrm{x}+\mathrm{1}−\mathrm{1}}{\:\sqrt{\mathrm{4}−\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }}\:\mathrm{dx} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}\left({x}+\mathrm{1}\right)}{\:\sqrt{\mathrm{4}−\left({x}+\mathrm{1}\right)^{\mathrm{2}}…

tan-x-sin-2-x-cos-3-x-cot-4-x-dx-

Question Number 144431 by imjagoll last updated on 25/Jun/21 $$\:\:\:\int\mathrm{tan}\:\mathrm{x}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{cot}\:^{\mathrm{4}} \mathrm{x}\:\mathrm{dx}\:=? \\ $$ Answered by iloveisrael last updated on 25/Jun/21 $$\:\int\:\frac{\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=\:\int\:\frac{\mathrm{cos}\:^{\mathrm{6}}…