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Question Number 44001 Answers: 0 Comments: 0

calculate A = ∫_0 ^1 (x/(arctanx))dx . ∫_0 ^1 ((arctanx)/x)dx

$${calculate}\:{A}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}}{{arctanx}}{dx}\:.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctanx}}{{x}}{dx} \\ $$

Question Number 43999 Answers: 0 Comments: 1

find the value of ∫_0 ^(π/2) (x/(√(1−cosx)))dx.

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{x}}{\sqrt{\mathrm{1}−{cosx}}}{dx}. \\ $$

Question Number 43992 Answers: 1 Comments: 1

Question Number 43991 Answers: 2 Comments: 0

∫ (1/(x^(1/2) + x^(1/3) )) dx

$$\int\:\frac{\mathrm{1}}{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\:\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }\:\:\:\mathrm{dx} \\ $$

Question Number 43990 Answers: 0 Comments: 1

Question Number 43987 Answers: 0 Comments: 2

Question Number 43981 Answers: 0 Comments: 4

∫(√(sin x)) dx

$$\int\sqrt{\mathrm{sin}\:{x}}\:{dx} \\ $$

Question Number 43980 Answers: 1 Comments: 0

Question Number 43969 Answers: 0 Comments: 0

Question Number 43971 Answers: 1 Comments: 0

Question Number 43966 Answers: 0 Comments: 0

Question Number 43956 Answers: 0 Comments: 0

Question Number 43945 Answers: 1 Comments: 1

Question Number 43944 Answers: 1 Comments: 0

If the points (−3, 5) , (4, −2) and (6, 2) are the vertices of a triangle. (i) Find the equation of the perpendicular bisector of the sides (ii) Find the coordinate of the circumcenter. (The circumcenter of a triangle is the point of intersection of the perpendicular bisector of the side (iii) Find the radius of the circumcircle.

Question Number 43939 Answers: 0 Comments: 1

find f(ξ) =∫_0 ^∞ (dt/(1+(t−iξ)^2 )) and calculate f^′ (ξ)

$${find}\:{f}\left(\xi\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\mathrm{1}+\left({t}−{i}\xi\right)^{\mathrm{2}} } \\ $$$${and}\:{calculate}\:{f}^{'} \left(\xi\right) \\ $$

Question Number 43938 Answers: 0 Comments: 1

calvulste A_n =∫_0 ^n t^2 [(1/((t+1)^3 ))]dt and lim_(n→+∞) A_n

$${calvulste}\:{A}_{{n}} =\int_{\mathrm{0}} ^{{n}} \:{t}^{\mathrm{2}} \left[\frac{\mathrm{1}}{\left({t}+\mathrm{1}\right)^{\mathrm{3}} }\right]{dt} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 43937 Answers: 1 Comments: 1

calculate ∫_0 ^1 ((2x+1)/(√(x^2 −2x+5)))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}}}{dx} \\ $$

Question Number 43935 Answers: 0 Comments: 1

find f(a) =∫_0 ^∞ ((1−cos^2 (ax))/x^2 )dx 2)calculate f^′ (a).

$${find}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{cos}^{\mathrm{2}} \left({ax}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({a}\right). \\ $$

Question Number 43934 Answers: 0 Comments: 1

find the value of ∫_0 ^(+∞) (dx/(1+x^4 +x^8 ))

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{+\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} \:+{x}^{\mathrm{8}} } \\ $$

Question Number 43923 Answers: 1 Comments: 0

A curve passes through the point (1,−11) and its gradient at any point is ax^2 +b, where a and b are constants. The tangent to the curve at the point (2,−16) is parallel to the x-axis. Find i. the values of a and b ii. the equation of the curve

$$\mathrm{A}\:\mathrm{curve}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},−\mathrm{11}\right)\:\mathrm{and}\:\mathrm{its} \\ $$$$\mathrm{gradient}\:\mathrm{at}\:\mathrm{any}\:\mathrm{point}\:\mathrm{is}\:\boldsymbol{\mathrm{a}}\mathrm{x}^{\mathrm{2}} +\boldsymbol{\mathrm{b}},\:\mathrm{where}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}\:\mathrm{are} \\ $$$$\mathrm{constants}.\:\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{2},−\mathrm{16}\right)\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{x}}-\mathrm{axis}.\:\mathrm{Find} \\ $$$$\mathrm{i}.\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{ii}.\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve} \\ $$

Question Number 43922 Answers: 0 Comments: 0