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AllQuestion and Answers: Page 228

Question Number 197225 Answers: 1 Comments: 0

Question Number 197212 Answers: 0 Comments: 1

Is ∫f(x)dx=∫_0 ^x lim_(x→t) f(x)dt?

$$\mathrm{Is}\:\int{f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{x}} \underset{{x}\rightarrow{t}} {\mathrm{lim}}{f}\left({x}\right){dt}? \\ $$

Question Number 197196 Answers: 1 Comments: 0

Question Number 197194 Answers: 1 Comments: 0

Question Number 197191 Answers: 1 Comments: 0

∫(1/(x^3 −3x+7))dx

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}}{dx} \\ $$

Question Number 197190 Answers: 1 Comments: 2

∫_0 ^1 ^3 (√(1−x^7 )) dx − ∫^1 _0 ^7 (√(1−x^3 )) dx = ?

$$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{\mathrm{1}−{x}^{\mathrm{7}} }\:{dx}\:−\:\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:^{\mathrm{7}} \sqrt{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:\:=\:\:? \\ $$

Question Number 197188 Answers: 1 Comments: 0

Question Number 197184 Answers: 1 Comments: 0

Show that log(−logi)=log((π/2))−i(π/2)

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{log}\left(−\mathrm{log}{i}\right)=\mathrm{log}\left(\frac{\pi}{\mathrm{2}}\right)−{i}\frac{\pi}{\mathrm{2}} \\ $$

Question Number 197185 Answers: 1 Comments: 0

Simplify (((((√2))^(√3) ∙((√3))^(√2) +((√2))^(√(12)) )/(((√6))^(√2) +((√2))^((√3)+(√2)) )))^(1/((√3)−(√2)))

$$\mathrm{Simplify} \\ $$$$\sqrt[{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}]{\frac{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \centerdot\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{12}}} }{\left(\sqrt{\mathrm{6}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}} }} \\ $$

Question Number 197177 Answers: 0 Comments: 0

find ∫_0 ^(π/2) ln^2 (cosx)dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{2}} \left({cosx}\right){dx} \\ $$

Question Number 197171 Answers: 1 Comments: 0

2^(log_3 (x^2 +1)) +2×(x^2 +1)^(log_3 2) =12 ⇒x=?

$$\mathrm{2}^{{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)} +\mathrm{2}×\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{log}_{\mathrm{3}} \mathrm{2}} \:=\mathrm{12} \\ $$$$\Rightarrow{x}=? \\ $$$$ \\ $$

Question Number 197589 Answers: 1 Comments: 0

how many natural numbers with 4 different digits are divisible by 3?

$${how}\:{many}\:{natural}\:{numbers}\:{with}\:\mathrm{4} \\ $$$${different}\:{digits}\:{are}\:{divisible}\:{by}\:\mathrm{3}? \\ $$

Question Number 197169 Answers: 2 Comments: 0

7x+4y=2

$$\mathrm{7}{x}+\mathrm{4}{y}=\mathrm{2} \\ $$

Question Number 197155 Answers: 1 Comments: 0

A bullet of mass 180g is fired horizontally into a fixed wooden block with a speed of 24m/s. if the bullet is brought to rest in 0.4sec by a constant resistance, calculate the distance moved by the bullet in the wood

$$\:{A}\:{bullet}\:{of}\:{mass}\:\mathrm{180}{g}\:{is}\:{fired}\: \\ $$$$\:{horizontally}\:{into}\:{a}\:{fixed}\:{wooden}\: \\ $$$$\:{block}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{24}{m}/{s}.\:{if}\:{the}\: \\ $$$${bullet}\:{is}\:{brought}\:{to}\:{rest}\:{in}\:\mathrm{0}.\mathrm{4}{sec}\:{by}\:{a} \\ $$$${constant}\:{resistance},\:{calculate}\:{the} \\ $$$${distance}\:{moved}\:{by}\:{the}\:{bullet}\:{in}\:{the} \\ $$$${wood} \\ $$

Question Number 197147 Answers: 2 Comments: 0

Question Number 197146 Answers: 1 Comments: 0

Find: Ω = ∫_0 ^( 1) ((Li(x))/(Ψ(x))) dx = ?

$$\mathrm{Find}:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}\left(\mathrm{x}\right)}{\Psi\left(\mathrm{x}\right)}\:\mathrm{dx}\:=\:? \\ $$

Question Number 197133 Answers: 1 Comments: 0

Question Number 197132 Answers: 1 Comments: 1

∫^( +∞) _( 0) (((ln(t+(√(1+t^2 ))))/t))^2 =(π^2 /2)

$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{\mathrm{ln}\left(\mathrm{t}+\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}{\mathrm{t}}\right)^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 197129 Answers: 2 Comments: 0

Question Number 197128 Answers: 1 Comments: 1

Question Number 197125 Answers: 1 Comments: 1

Question Number 197113 Answers: 1 Comments: 0

Prove that ∫^( +∞) _( 0) (((ln(t+(√(1+t^2 ))))/t))dt=(π^2 /2)

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left(\frac{{ln}\left({t}+\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\right)}{{t}}\right){dt}=\frac{\pi^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 197112 Answers: 2 Comments: 0

Question Number 197111 Answers: 1 Comments: 0

$$\:\:\:\:\:\:\cancel{ } \\ $$

Question Number 197110 Answers: 1 Comments: 0

Question Number 197104 Answers: 0 Comments: 3

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