Question and Answers Forum

AllQuestion and Answers: Page 62

Question Number 218673 Answers: 3 Comments: 1

Question Number 218672 Answers: 2 Comments: 0

Question Number 218662 Answers: 4 Comments: 0

Prove: ∫^∞ _0 ((sin(x))/x) dx = (π/2)

$$\: \\ $$$$\:\:\:\:{Prove}:\:\:\:\:\underset{\mathrm{0}} {\int}^{\infty} \:\frac{{sin}\left({x}\right)}{{x}}\:{dx}\:=\:\frac{\pi}{\mathrm{2}} \\ $$$$ \\ $$

Question Number 218658 Answers: 2 Comments: 0

Question Number 218769 Answers: 1 Comments: 0

Fourier Series f(θ)=e^(izsin(θ))

$$\mathrm{Fourier}\:\mathrm{Series}\:{f}\left(\theta\right)={e}^{\boldsymbol{{i}}{z}\mathrm{sin}\left(\theta\right)} \\ $$

Question Number 218656 Answers: 2 Comments: 0

resolve the equation with unknow p P is polynom 1) P(X^2 )=(X^2 +1)P(X) 2) P 0P =P

$${resolve}\:{the}\:{equation}\:{with}\:{unknow}\:{p} \\ $$$${P}\:\:{is}\:{polynom}\: \\ $$$$\left.\mathrm{1}\right)\:{P}\left({X}^{\mathrm{2}} \right)=\left({X}^{\mathrm{2}} +\mathrm{1}\right){P}\left({X}\right) \\ $$$$\left.\mathrm{2}\right)\:{P}\:\mathrm{0}{P}\:={P} \\ $$

Question Number 218652 Answers: 0 Comments: 4

Angle of incidence is 40° if the direction of the incidence ray is constant and the mirror is rotated through 20° the angle between the new reflected ray and new normal is

Question Number 218651 Answers: 1 Comments: 0

Question Number 218650 Answers: 1 Comments: 0

Question Number 218649 Answers: 2 Comments: 0

Question Number 218648 Answers: 1 Comments: 0

Question Number 218646 Answers: 1 Comments: 1

Question Number 218645 Answers: 4 Comments: 0

Question Number 218644 Answers: 2 Comments: 0

Question Number 218636 Answers: 1 Comments: 0

Question Number 218629 Answers: 1 Comments: 0

Question Number 218626 Answers: 0 Comments: 0

Prove that for all real numbers a and b with a<b, the following inequality holds; (∫_a ^b 1 dx)^3 ≤ (b−a)(∫_a ^b (x−a+1)^2 dx)(∫_(a ) ^b (1/((a−x+1)^3 ))dx)

$$ \\ $$$$\:{Prove}\:{that}\:{for}\:{all}\:{real}\:{numbers}\:{a}\:{and}\:{b} \\ $$$${with}\:{a}<{b},\:{the}\:{following}\:{inequality}\:{holds}; \\ $$$$\left(\int_{{a}} ^{{b}} \mathrm{1}\:{dx}\right)^{\mathrm{3}} \leqslant\:\left({b}−{a}\right)\left(\int_{{a}} ^{{b}} \left({x}−{a}+\mathrm{1}\right)^{\mathrm{2}} {dx}\right)\left(\int_{{a}\:} ^{{b}} \frac{\mathrm{1}}{\left({a}−{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\right) \\ $$$$ \\ $$

Question Number 218624 Answers: 1 Comments: 0

Prove; ∫^e _(1/e) (t^2 /e^t^(2 ) ) dt ≤ 1− (1/e^(2 ) ) e−the base of natural logarithm

$$ \\ $$$$\:\:\:\:{Prove};\:\underset{\frac{\mathrm{1}}{{e}}} {\int}^{{e}} \:\frac{{t}^{\mathrm{2}} }{{e}^{{t}^{\mathrm{2}\:} } }\:{dt}\:\leqslant\:\mathrm{1}−\:\frac{\mathrm{1}}{{e}^{\mathrm{2}\:\:} } \\ $$$$\:\:\:{e}−{the}\:{base}\:{of}\:{natural}\:{logarithm} \\ $$$$ \\ $$

Question Number 219017 Answers: 0 Comments: 0