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Question Number 35471 Answers: 0 Comments: 0

∫_a ^b f(x)dx=area under the curve but say why what is the meaning of ∫ ←this sign

$$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}={area}\:{under}\:{the}\:{curve}\:{but}\:{say}\:{why} \\ $$$${what}\:{is}\:{the}\:{meaning}\:{of}\:\int\:\leftarrow{this}\:{sign} \\ $$

Question Number 35470 Answers: 2 Comments: 0

prove sin0^o =0 and cos0^o =1

$${prove}\:{sin}\mathrm{0}^{{o}} =\mathrm{0}\:\:{and}\:{cos}\mathrm{0}^{{o}} =\mathrm{1} \\ $$

Question Number 35469 Answers: 0 Comments: 0

find distance between (x_(1,) y_1 ) and (x_2 ,y_2 ) when x axis and y axis inclined ai angle θ

$${find}\:{distance}\:{between}\:\left({x}_{\mathrm{1},} {y}_{\mathrm{1}} \right)\:{and}\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right)\:{when} \\ $$$${x}\:{axis}\:{and}\:{y}\:{axis}\:{inclined}\:{ai}\:{angle}\:\theta \\ $$

Question Number 35467 Answers: 1 Comments: 0

If x = 32 − 16 ÷ 2 × 4, then x=

$$\mathrm{If}\:\:{x}\:=\:\mathrm{32}\:−\:\mathrm{16}\:\boldsymbol{\div}\:\mathrm{2}\:×\:\mathrm{4},\:\mathrm{then}\:{x}= \\ $$

Question Number 35461 Answers: 1 Comments: 0

Question Number 35460 Answers: 1 Comments: 1

Find the values of k for which the equation (((k −3)),((10 −k+1)) ) ((x),(y) ) = (((k−1)),(8) ) have a) a unique solution b) no solution c)an infinite solution hence Find the image of the point (3,1) after reflection in the line with equation a) x=1 b) y= −1 c) y+x= 1

$${Find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which} \\ $$$${the}\:{equation}\: \\ $$$$\begin{pmatrix}{{k}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\\{\mathrm{10}\:\:\:\:\:\:\:−{k}+\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{k}−\mathrm{1}}\\{\mathrm{8}}\end{pmatrix} \\ $$$${have} \\ $$$$\left.{a}\right)\:{a}\:\:{unique}\:{solution} \\ $$$$\left.{b}\right)\:{no}\:{solution} \\ $$$$\left.{c}\right){an}\:{infinite}\:{solution} \\ $$$${hence} \\ $$$${Find}\:{the}\:{image}\:{of}\:{the}\:{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right)\:{after}\:{reflection}\:{in}\:{the}\:{line} \\ $$$${with}\:{equation} \\ $$$$\left.{a}\left.\right)\left.\:{x}=\mathrm{1}\:\:\:\:{b}\right)\:{y}=\:−\mathrm{1}\:\:\boldsymbol{{c}}\right)\:\boldsymbol{{y}}+\boldsymbol{{x}}=\:\mathrm{1} \\ $$

Question Number 35456 Answers: 2 Comments: 0

∫(dx/(x(x^(2018) +1)))

$$\int\frac{{dx}}{{x}\left({x}^{\mathrm{2018}} +\mathrm{1}\right)} \\ $$

Question Number 35446 Answers: 1 Comments: 1

Question Number 35440 Answers: 1 Comments: 2

find the value of ∫_0 ^∞ (dx/((2x^2 +1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 35439 Answers: 0 Comments: 1

Question Number 35438 Answers: 0 Comments: 1

let m>0 and 0<a<b 1) calculate ∫_0 ^∞ ((cos(mx))/((x^2 +a^2 )(x^2 +b^2 )))dx 2)find the value of ∫_0 ^∞ ((cos(2x))/((x^2 +1)(x^2 +3)))dx

$${let}\:{m}>\mathrm{0}\:{and}\:\mathrm{0}<{a}<{b}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{cos}\left({mx}\right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:\:+\mathrm{3}\right)}{dx} \\ $$

Question Number 35430 Answers: 1 Comments: 1

Question Number 35429 Answers: 1 Comments: 1

find ∫_0 ^1 ((2x−1)/(√(x^2 +6))) dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} \:\:+\mathrm{6}}}\:{dx} \\ $$

Question Number 35428 Answers: 1 Comments: 1

find ∫ ((x+3)/(√(x^2 +x −1)))dx

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

Question Number 35427 Answers: 1 Comments: 1

calculate ∫_2 ^5 (e^(√(x+1)) /(√(x+1)))dx

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

Question Number 35425 Answers: 1 Comments: 0

Given that a number is a factor of 144 and the square of the number added to five times the number is ≥ −6 find the number

$$\:{Given}\:{that}\:{a}\:{number}\:{is}\:{a}\:{factor}\: \\ $$$${of}\:\mathrm{144}\:{and}\:{the}\:{square}\:{of}\:{the}\:{number} \\ $$$${added}\:{to}\:{five}\:{times}\:{the}\:{number} \\ $$$${is}\:\geqslant\:−\mathrm{6}\:{find}\:{the}\:{number} \\ $$

Question Number 35426 Answers: 1 Comments: 2

find the value of x if the inverse of the matrix (((x+5 2)),((7 x)) ) is (((0 0)),((0 0)) )

$${find}\:{the}\:{value}\:{of}\:{x}\:{if}\:{the}\:{inverse} \\ $$$${of}\:{the}\:{matrix}\:\begin{pmatrix}{{x}+\mathrm{5}\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{7}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}}\end{pmatrix}\:{is} \\ $$$$\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 35422 Answers: 0 Comments: 2

Question Number 35416 Answers: 1 Comments: 2

let −1≤x≤1 simplify A=sin{ arcsinx +2arcsin)(1−x)}

$${let}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}\:{simplify} \\ $$$$\left.{A}={sin}\left\{\:{arcsinx}\:\:+\mathrm{2}{arcsin}\right)\left(\mathrm{1}−{x}\right)\right\} \\ $$

Question Number 35412 Answers: 1 Comments: 2

evaluate ∫(√((t^2 +1+(3/4)t))) dt

$$\boldsymbol{\mathrm{evaluate}}\:\int\sqrt{\left(\boldsymbol{\mathrm{t}}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}\boldsymbol{\mathrm{t}}\right)}\:\boldsymbol{\mathrm{dt}} \\ $$

Question Number 35646 Answers: 1 Comments: 2

Question Number 35645 Answers: 1 Comments: 0

sketch the graph of f(x)=2−x−x^2 then state its domain and range

$$\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{{x}}\right)=\mathrm{2}−\boldsymbol{{x}}−\boldsymbol{{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{state}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{domain}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{range}} \\ $$

Question Number 35390 Answers: 1 Comments: 6

Question Number 35384 Answers: 1 Comments: 1

((−1+i(√3)))^(1/6) =....??

$$\sqrt[{\mathrm{6}}]{−\mathrm{1}+{i}\sqrt{\mathrm{3}}}\:=....?? \\ $$

Question Number 35379 Answers: 2 Comments: 3

∫_0 ^( 1) t^2 (√(1+t^2 )) dt = ?

$$\int_{\mathrm{0}} ^{\:\:\mathrm{1}} {t}^{\mathrm{2}} \sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt}\:=\:? \\ $$

Question Number 35367 Answers: 2 Comments: 0

Q_(3 ) . a number is a factor of 6 the square of the number added to 5 times thenumber is same as −6 find the number.

$${Q}_{\mathrm{3}\:} .\:{a}\:{number}\:{is}\:{a}\:{factor}\:{of}\:\mathrm{6} \\ $$$$\:{the}\:{square}\:{of}\:{the}\:{number}\:{added}\: \\ $$$${to}\:\mathrm{5}\:{times}\:{thenumber}\:{is}\:{same}\:{as} \\ $$$$−\mathrm{6}\:{find}\:{the}\:{number}. \\ $$

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