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Question Number 54176 Answers: 0 Comments: 0
$${what}\:{is}\:{the}\:{integral}\:{vslue}\:{of}\:\int{x}!{dx} \\ $$
Question Number 54170 Answers: 1 Comments: 1
Question Number 54167 Answers: 1 Comments: 2
Question Number 54163 Answers: 0 Comments: 1
Question Number 54160 Answers: 1 Comments: 1
Question Number 54156 Answers: 0 Comments: 1
$$\mathrm{Please}\:\mathrm{sirs},\:\:\mathrm{How}\:\mathrm{is},\:\:\:\:\:\:−\:\mathrm{cot}\left(\alpha\right)\:\:=\:\:\mathrm{tan}\left(\frac{\mathrm{1}}{\mathrm{2}}\pi\:+\:\alpha\right)\:\:???? \\ $$
Question Number 54152 Answers: 0 Comments: 3
Question Number 54137 Answers: 1 Comments: 2
Question Number 54126 Answers: 1 Comments: 0
$${Prove}\:{that} \\ $$$$\frac{\mathrm{sin}\:\mathrm{19}\theta}{\mathrm{sin}\:\theta}\:=\:\mathrm{cos}\left(−\mathrm{18}\theta\right)+\mathrm{cos}\left(−\mathrm{16}\theta\right)+... \\ $$$$\:\:\:...+\:\mathrm{cos}\left(−\mathrm{2}\theta\right)+\mathrm{1}+\mathrm{cos}\left(\mathrm{2}\theta\right)+....+\mathrm{cos}\left(\mathrm{18}\theta\right). \\ $$
Question Number 54116 Answers: 0 Comments: 0
Question Number 54102 Answers: 1 Comments: 3
$$\mathrm{the}\:\mathrm{absolute}\:\mathrm{value} \\ $$$$\int_{\mathrm{10}} ^{\mathrm{19}} \frac{\mathrm{cos}\:{x}}{\mathrm{1}+{x}^{\mathrm{8}} }\:{dx}\:\mathrm{is}... \\ $$
Question Number 54093 Answers: 0 Comments: 8
$$\mathrm{If}\:\:\:\:\:\:\mathrm{tan}\left(\mathrm{z}\right)\:\:=\:\:\mathrm{2},\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{z} \\ $$
Question Number 54074 Answers: 1 Comments: 5
$${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{dx}}{\sqrt{\mathrm{1}+{x}}+\sqrt{\mathrm{1}−{x}}+\mathrm{2}}\: \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \frac{{ln}\left(\mathrm{1}+\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right) \\ $$$$\:\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{3}} {x}}}\left(\left(\mathrm{3}\pi\mathrm{cos}{x}+\mathrm{4sin}{x}\right)\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{4}\right){dx} \\ $$$$\left.\mathrm{4}\right) \\ $$$$\int_{\mathrm{0}} ^{\:\pi} \:\frac{{x}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} {x}−{x}\mathrm{sin}{x}−\mathrm{cos}{x}−\mathrm{1}}{\left(\mathrm{1}+{x}\mathrm{sin}{x}\right)^{\mathrm{2}} }\:{dx}. \\ $$
Question Number 54073 Answers: 1 Comments: 0
Question Number 54070 Answers: 2 Comments: 7
$${Evaluate}\:: \\ $$$$\left.\mathrm{1}\right) \\ $$$$\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \mathrm{cot}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\right).\left(\mathrm{co}{t}^{−\mathrm{1}} \frac{{x}}{\sqrt{\mathrm{1}−\left({x}^{\mathrm{2}} \right)^{\mid{x}\mid} }}\right){dx} \\ $$$$\left.\mathrm{2}\right) \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{10}\right)\theta}{\mathrm{sin}^{\mathrm{2}} \theta}\:{d}\theta \\ $$$$\left.\mathrm{3}\right) \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{{ln}\left({cotx}\right)}{\left(\left(\mathrm{sin}{x}\right)^{\mathrm{2009}} +\left(\mathrm{cos}{x}\right)^{\mathrm{2009}} \right)^{\mathrm{2}} }.\left(\mathrm{sin2}{x}\right)^{\mathrm{2008}} {dx} \\ $$$$\left.\mathrm{4}\right) \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\mathrm{4}{x}+\mathrm{10}}{\left({x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{6}\right)^{\mathrm{2}} }\:{dx}. \\ $$
Question Number 54068 Answers: 1 Comments: 2
Question Number 54061 Answers: 0 Comments: 8
Question Number 54051 Answers: 1 Comments: 0
Question Number 54045 Answers: 2 Comments: 1
Question Number 54034 Answers: 0 Comments: 1
$$\mathrm{If}\:{f}\left({x}\right)={f}\left({a}+{b}−{x}\right),\:\mathrm{then}\:\underset{{a}} {\overset{{b}} {\int}}\:{x}\:{f}\left({x}\right)\:{dx}\:= \\ $$
Question Number 54033 Answers: 2 Comments: 1
$$\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:{dx}\:= \\ $$
Question Number 54032 Answers: 0 Comments: 4
$$\underset{−\mathrm{2}\:} {\overset{\mathrm{2}} {\int}}\:\mathrm{min}\:\left({x}−\left[{x}\right],\:−{x}−\left[−{x}\right]\right){dx}\:\mathrm{equals}\:\left[{x}\right] \\ $$$$\mathrm{represents}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{less}\:\mathrm{than}\:\mathrm{or} \\ $$$$\left.\mathrm{equal}\:\mathrm{to}\:{x}\right). \\ $$
Question Number 54031 Answers: 1 Comments: 0
$$\mathrm{If}\:\:{f}\left({a}+{b}−{x}\right)=\:{f}\left({x}\right),\:\mathrm{then}\:\underset{{a}} {\overset{{b}} {\int}}\:{x}\:{f}\left({x}\right)\:{dx}\:= \\ $$
Question Number 54029 Answers: 1 Comments: 1
$$\underset{\:\mathrm{3}} {\overset{\mathrm{9}} {\int}}\:\frac{\sqrt{{x}}}{\sqrt{\mathrm{12}−{x}}\:+\:\sqrt{{x}}}\:{dx}\:=\:\mathrm{9} \\ $$
Question Number 54028 Answers: 1 Comments: 0
$$\mathrm{If}\:\mathrm{for}\:\mathrm{every}\:\mathrm{integer}\:{n},\:\underset{{n}} {\overset{{n}+\mathrm{1}} {\int}}{f}\left({x}\right)\:{dx}\:=\:{n}^{\mathrm{2}} , \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{−\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}= \\ $$
Question Number 54025 Answers: 1 Comments: 1
$$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C},\:\mathrm{D}\:\mathrm{have}\:\mathrm{coordinates} \\ $$$$\left(−\mathrm{7},\mathrm{9}\right),\:\left(\mathrm{3},\mathrm{4}\right),\:\left(\mathrm{1},\mathrm{12}\right),\:\mathrm{and}\:\left(−\mathrm{2},−\mathrm{9}\right). \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{linePQ}\:\mathrm{where}\:\mathrm{P} \\ $$$$\mathrm{devides}\:\mathrm{AB}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{2}:\mathrm{3}\:\mathrm{and}\:\mathrm{devides} \\ $$$$\mathrm{CD}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{1}:−\mathrm{4}. \\ $$
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