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Question Number 31145 Answers: 1 Comments: 0

Given ∫_0 ^1 f(x) dx = (((2018)),(( 0)) ) + (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) + ... + (1/(2019)) (((2018)),((2018)) ) ∫_0 ^1 g(x) dx = (((2018)),(( 0)) ) − (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) − ... + (1/(2019)) (((2018)),((2018)) ) h(x) is an odd function Then what is the value of ∫_(−3) ^( 3) f(x).g(x).h(x) dx ?

$$\mathrm{Given} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right)\:{dx}\:=\:\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{2019}}\begin{pmatrix}{\mathrm{2018}}\\{\mathrm{2018}}\end{pmatrix} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right)\:{dx}\:=\:\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{2018}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:−\:...\:+\:\frac{\mathrm{1}}{\mathrm{2019}}\begin{pmatrix}{\mathrm{2018}}\\{\mathrm{2018}}\end{pmatrix} \\ $$$${h}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{odd}\:\mathrm{function} \\ $$$$\mathrm{Then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{−\mathrm{3}} ^{\:\mathrm{3}} \:{f}\left({x}\right).{g}\left({x}\right).{h}\left({x}\right)\:{dx}\:? \\ $$

Question Number 31144 Answers: 0 Comments: 2

A mass oscillating on a spring has amplitude of 1.2m and a period of 2.0s. (a)Deduce the equation for the displacement x if the timing starts at the instant where the mass has its maximum displacement. b)calculate the time interval c)the velocity at this position.

$${A}\:{mass}\:{oscillating}\:{on}\:{a}\:{spring} \\ $$$${has}\:{amplitude}\:{of}\:\mathrm{1}.\mathrm{2}{m}\:{and}\:{a} \\ $$$${period}\:{of}\:\mathrm{2}.\mathrm{0}{s}. \\ $$$$\left({a}\right){Deduce}\:{the}\:{equation}\:{for}\:{the} \\ $$$${displacement}\:{x}\:{if}\:{the}\:{timing}\:{starts} \\ $$$${at}\:{the}\:{instant}\:{where}\:{the}\:{mass} \\ $$$${has}\:{its}\:{maximum}\:{displacement}. \\ $$$$\left.{b}\right){calculate}\:{the}\:{time}\:{interval} \\ $$$$\left.{c}\right){the}\:{velocity}\:{at}\:{this}\:{position}. \\ $$

Question Number 31143 Answers: 1 Comments: 0

A cyclist is travelling down a hill at a speed of 9.2m/s . The hillside makes an angle of 6.3° with the horizontal .Calculate, for the cyclist: (i)the vertical speed (ii)horizontal speed

$${A}\:{cyclist}\:{is}\:{travelling}\:{down}\:{a} \\ $$$${hill}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{9}.\mathrm{2}{m}/{s}\:.\:{The} \\ $$$${hillside}\:{makes}\:{an}\:{angle}\:{of}\:\mathrm{6}.\mathrm{3}° \\ $$$${with}\:{the}\:{horizontal}\:.{Calculate}, \\ $$$${for}\:{the}\:{cyclist}: \\ $$$$\left({i}\right){the}\:{vertical}\:{speed} \\ $$$$\left({ii}\right){horizontal}\:{speed} \\ $$

Question Number 31141 Answers: 1 Comments: 0

using the limit defination find the area of f(x)= cos(x) [0,π/2]

$$\boldsymbol{{using}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\:\boldsymbol{{defination}} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{area}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\:\:\left[\mathrm{0},\pi/\mathrm{2}\right] \\ $$

Question Number 31004 Answers: 1 Comments: 0