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Question Number 83824 Answers: 2 Comments: 1

Question Number 83822 Answers: 1 Comments: 1

Question Number 83819 Answers: 1 Comments: 0

If the function of f is continous in R and ∫ _0 ^( x) f(t)dt = ∫ _x ^( 1) t^2 f(t) dt + 2x^2 +4x+c , ∀x∈R. The value of constant c is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}\:\mathrm{is}\:\mathrm{continous} \\ $$$$\mathrm{in}\:\mathbb{R}\:\mathrm{and}\:\int\underset{\mathrm{0}} {\overset{\:\mathrm{x}} {\:}}\:\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt}\:=\:\int\underset{\mathrm{x}} {\overset{\:\mathrm{1}} {\:}}\mathrm{t}^{\mathrm{2}} \mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:+\: \\ $$$$\mathrm{2x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{c}\:,\:\forall\mathrm{x}\in\mathbb{R}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{constant}\:\mathrm{c}\:\mathrm{is}\: \\ $$

Question Number 83812 Answers: 0 Comments: 0

Question Number 83811 Answers: 0 Comments: 2

Question Number 83807 Answers: 2 Comments: 1

Evaluate: ∫ (( 1)/(ax^2 +bx+c))dx

$$\:\:\boldsymbol{\mathrm{Evaluate}}: \\ $$$$\:\:\int\:\:\frac{\:\mathrm{1}}{\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\boldsymbol{\mathrm{bx}}+\boldsymbol{\mathrm{c}}}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 83805 Answers: 3 Comments: 1

∫_0 ^(π/2) ((sin^2 (x))/(sin(x)+cos(x))) dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{\mathrm{2}} \left({x}\right)}{{sin}\left({x}\right)+{cos}\left({x}\right)}\:{dx} \\ $$

Question Number 83892 Answers: 0 Comments: 0

∫(du/(u−u^2 ))

$$\int\frac{\mathrm{du}}{\mathrm{u}−\mathrm{u}^{\mathrm{2}} } \\ $$

Question Number 83891 Answers: 0 Comments: 3

1111^(2019) mod 11111=....?

$$ \\ $$$$ \\ $$$$\mathrm{1111}^{\mathrm{2019}} \:\mathrm{mod}\:\mathrm{11111}=....? \\ $$

Question Number 83791 Answers: 2 Comments: 2

Let x, y are two different real numbers satisfy the equation (√(y+4)) = x−4 and (√(x+4)) = y−4. The value of x^3 +y^3 mod(x^3 y^3 ) is

$$\mathrm{Let}\:\mathrm{x},\:\mathrm{y}\:\mathrm{are}\:\mathrm{two}\:\mathrm{different}\:\mathrm{real} \\ $$$$\mathrm{numbers}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\sqrt{\mathrm{y}+\mathrm{4}}\:=\:\mathrm{x}−\mathrm{4}\:\mathrm{and}\:\sqrt{\mathrm{x}+\mathrm{4}}\:=\:\mathrm{y}−\mathrm{4}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} \:\mathrm{mod}\left(\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} \right)\:\mathrm{is} \\ $$

Question Number 83787 Answers: 1 Comments: 0

find the value of abc if (√(2+(√(2^2 +(√(2^3 +2^4 +(√(...)))))))) = (((√a)+(√b))/c)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{abc}\:\mathrm{if}\: \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}^{\mathrm{2}} +\sqrt{\mathrm{2}^{\mathrm{3}} +\mathrm{2}^{\mathrm{4}} +\sqrt{...}}}}\:=\:\frac{\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}}{\mathrm{c}} \\ $$

Question Number 83786 Answers: 2 Comments: 0

(x^2 /(log_((5−x)) (x))) ≤ (5x−4) log_x (5−x)

$$\frac{{x}^{\mathrm{2}} }{\mathrm{log}_{\left(\mathrm{5}−{x}\right)} \:\left({x}\right)}\:\leqslant\:\left(\mathrm{5}{x}−\mathrm{4}\right)\:\mathrm{log}_{{x}} \:\left(\mathrm{5}−{x}\right)\: \\ $$

Question Number 83782 Answers: 0 Comments: 1

f^((5)) (x) = 4^(−sin x) f^((7)) (x) =?

$$\mathrm{f}^{\left(\mathrm{5}\right)} \:\left(\mathrm{x}\right)\:=\:\mathrm{4}^{−\mathrm{sin}\:\mathrm{x}} \\ $$$$\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{x}\right)\:=?\: \\ $$

Question Number 83781 Answers: 1 Comments: 2

∫ _0^(π/2) (1/(4sin^2 x+5cos^2 x)) dx

$$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{5cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 83774 Answers: 1 Comments: 0

Given 2(√(log_3 x−1)) − log_3 x^3 +8 > 0 have the solution a ≤ x < b. what is b ?

$$\mathrm{Given}\:\mathrm{2}\sqrt{\mathrm{log}_{\mathrm{3}} \:{x}−\mathrm{1}}\:−\:\mathrm{log}_{\mathrm{3}} \:{x}^{\mathrm{3}} \:+\mathrm{8}\:>\:\mathrm{0} \\ $$$${have}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{a}\:\leqslant\:{x}\:<\:{b}.\: \\ $$$${what}\:{is}\:{b}\:?\: \\ $$

Question Number 83767 Answers: 2 Comments: 1

Question Number 83759 Answers: 2 Comments: 3

3^x 8^(x/(x+2)) =6

$$\mathrm{3}^{{x}} \:\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6} \\ $$

Question Number 83756 Answers: 0 Comments: 3

Find all real solutions of (x, y) such that x + 3y + (4/(x + y)) = 5 y + 3x + (5/(x + y)) = 7

$${Find}\:\:{all}\:\:{real}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\mathrm{3}{y}\:+\:\frac{\mathrm{4}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:{y}\:+\:\mathrm{3}{x}\:+\:\frac{\mathrm{5}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{7} \\ $$

Question Number 83750 Answers: 0 Comments: 0

I=∫e^x tan(x) dx

$${I}=\int{e}^{{x}} \:{tan}\left({x}\right)\:{dx} \\ $$

Question Number 83739 Answers: 0 Comments: 3

what is minimum value of f(x) = (sin x+ csc x )^2 +sec x + cos x

$$\mathrm{what}\:\mathrm{is}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\left(\mathrm{sin}\:\mathrm{x}+\:\mathrm{csc}\:\mathrm{x}\:\right)^{\mathrm{2}} +\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x} \\ $$

Question Number 83737 Answers: 0 Comments: 0

∫ (x^3 /(x^4 +cos x)) dx ?

$$\int\:\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{4}} +\mathrm{cos}\:{x}}\:{dx}\:? \\ $$

Question Number 83721 Answers: 3 Comments: 8

Question Number 83719 Answers: 2 Comments: 1

Question. ^(Show that ∫_0 ^(Π/2) ((cosx)/(3+cos^2 x))dx=(1/4)ln3)

$${Question}.\:\:\:\:\:\:\:\:\overset{{Show}\:\:{that}\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \frac{{cosx}}{\mathrm{3}+{cos}^{\mathrm{2}} {x}}{dx}=\frac{\mathrm{1}}{\mathrm{4}}{ln}\mathrm{3}} {\:} \\ $$

Question Number 83717 Answers: 0 Comments: 0

Question Number 83713 Answers: 1 Comments: 8

∫(dx/(√(x+(√(x+(√x)))))) pleas sir help me

$$\int\frac{{dx}}{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:\:\:{pleas}\:{sir}\:{help}\:{me} \\ $$

Question Number 83710 Answers: 0 Comments: 1

lim_(x→∞) (((1+(√5))^x −(1−(√5))^x )/((1+(√5))^(x−1) −(1−(√5))^(x−1) )) = ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} −\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)^{{x}−\mathrm{1}} }\:=\:? \\ $$

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