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Question Number 82617 Answers: 1 Comments: 0

∫sin (101x)(sinx)^(99) dx

$$\int\mathrm{sin}\:\left(\mathrm{101}{x}\right)\left({sinx}\right)^{\mathrm{99}} {dx} \\ $$

Question Number 82616 Answers: 0 Comments: 0

Find the normalization constant ψ_((φ,θ)) =Ne^(iφ) sinθ

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{normalization}\:\mathrm{constant}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\psi_{\left(\phi,\theta\right)} =\mathrm{Ne}^{\mathrm{i}\phi} \mathrm{sin}\theta \\ $$

Question Number 82614 Answers: 1 Comments: 0

∫ ((sin 2x)/(sin 5x sin 3x)) dx ?

$$\int\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{sin}\:\mathrm{5}{x}\:\mathrm{sin}\:\mathrm{3}{x}}\:{dx}\:?\: \\ $$

Question Number 82609 Answers: 0 Comments: 1

Question Number 82608 Answers: 0 Comments: 1

Question Number 82607 Answers: 1 Comments: 5

Question Number 82685 Answers: 0 Comments: 0

∫_0 ^5 (((3x^3 −x^4 ))^(1/4) /(5−x))dx

$$\int_{\mathrm{0}} ^{\mathrm{5}} \:\frac{\sqrt[{\mathrm{4}}]{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{4}} }}{\mathrm{5}−{x}}{dx} \\ $$

Question Number 82604 Answers: 1 Comments: 0

∫ ((cos (5x)+cos (4x) dx)/(1−2cos (3x))) =

$$\int\:\frac{\mathrm{cos}\:\left(\mathrm{5}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}\right)\:{dx}}{\mathrm{1}−\mathrm{2cos}\:\left(\mathrm{3}{x}\right)}\:=\: \\ $$

Question Number 82596 Answers: 0 Comments: 4

Question Number 82593 Answers: 0 Comments: 3

Question Number 82591 Answers: 0 Comments: 12

A closed surface is defined in spherical coordinates by 3<r<5 , 0.1π<θ<0.3π, 1.2π<φ<1.6π. Find the total surface area.

$${A}\:{closed}\:{surface}\:{is}\:{defined}\:{in}\:{spherical} \\ $$$${coordinates}\:{by}\:\mathrm{3}<{r}<\mathrm{5}\:,\:\mathrm{0}.\mathrm{1}\pi<\theta<\mathrm{0}.\mathrm{3}\pi, \\ $$$$\mathrm{1}.\mathrm{2}\pi<\phi<\mathrm{1}.\mathrm{6}\pi.\:\boldsymbol{{F}}{ind}\:{the}\:{total}\:{surface} \\ $$$${area}. \\ $$

Question Number 82589 Answers: 0 Comments: 1

Question Number 82583 Answers: 0 Comments: 0

Question Number 82582 Answers: 0 Comments: 2

solve x^3 −3x+1=0

$${solve} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 82579 Answers: 1 Comments: 0

if y=cos(ln(x))+sin(ln(x)) show that y′′+y^′ +y=0

$${if}\:{y}={cos}\left({ln}\left({x}\right)\right)+{sin}\left({ln}\left({x}\right)\right) \\ $$$${show}\:{that} \\ $$$${y}''+{y}^{'} +{y}=\mathrm{0} \\ $$

Question Number 82577 Answers: 0 Comments: 3

∫((2−(√(x+3)))/(2+(√(x−3)))) dx

$$\int\frac{\mathrm{2}−\sqrt{{x}+\mathrm{3}}}{\mathrm{2}+\sqrt{{x}−\mathrm{3}}}\:{dx} \\ $$

Question Number 82574 Answers: 0 Comments: 0

Question Number 82573 Answers: 0 Comments: 4

Question Number 82572 Answers: 0 Comments: 1

Question Number 82571 Answers: 0 Comments: 0

Question Number 82570 Answers: 0 Comments: 1

if f(x) = f(x+1) − x find f(x)

$${if}\:{f}\left({x}\right)\:=\:{f}\left({x}+\mathrm{1}\right)\:−\:{x}\: \\ $$$${find}\:{f}\left({x}\right)\: \\ $$

Question Number 82568 Answers: 1 Comments: 0

∫ (1/(tan x+cot x+sec x+cosec x)) dx ?

$$\int\:\frac{\mathrm{1}}{\mathrm{tan}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}+\mathrm{cosec}\:{x}}\:{dx}\:? \\ $$

Question Number 82566 Answers: 2 Comments: 1

∫ (√((x+1)/x)) dx = ?

$$\int\:\sqrt{\frac{{x}+\mathrm{1}}{{x}}}\:{dx}\:=\:? \\ $$

Question Number 82564 Answers: 0 Comments: 0

Question Number 82562 Answers: 0 Comments: 0

Question Number 82561 Answers: 1 Comments: 0

a polynomial gives a remainder of −x−1 when divided by x^(2.) and a remainder of −1 when divided by x−1 . what is the remainder when the polynomial divided by x^2 (x−1) ?

$${a}\:{polynomial}\:{gives}\:{a}\:{remainder} \\ $$$${of}\:−{x}−\mathrm{1}\:{when}\:{divided}\:{by}\:{x}^{\mathrm{2}.} \\ $$$${and}\:\:{a}\:{remainder}\:{of}\:−\mathrm{1}\:{when}\: \\ $$$${divided}\:{by}\:{x}−\mathrm{1}\:.\:{what}\:{is}\:{the}\: \\ $$$${remainder}\:{when}\:{the}\:{polynomial} \\ $$$${divided}\:{by}\:{x}^{\mathrm{2}} \left({x}−\mathrm{1}\right)\:? \\ $$

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