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Question Number 152795 Answers: 1 Comments: 0

𝛗=∫_0 ^( ∞) ((sin(x ))/x)(((a^( 2) +cos^( 2) (x))/(b^( 2) + cos^( 2) (x ))))dx=?

$$ \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\:\right)}{{x}}\left(\frac{{a}^{\:\mathrm{2}} +{cos}^{\:\mathrm{2}} \left({x}\right)}{{b}^{\:\mathrm{2}} +\:{cos}^{\:\mathrm{2}} \left({x}\:\right)}\right){dx}=? \\ $$$$ \\ $$

Question Number 152779 Answers: 0 Comments: 4

Question Number 152778 Answers: 0 Comments: 0

Solve .......... Ω := ∫_0 ^( 1) x. sin( ln (x ))dx =^? ((−1)/( 5)) solution.... Ω :=^(i.b.p) [ (x^( 2) /2) . sin(ln(x))]_0 ^( 1) −(1/2)∫_0 ^( 1) x.cos( ln (x ))dx := ((−1)/2) ∫_0 ^( 1) x. cos (ln (x ))dx :=^(i.b.p) ((−1)/2) {[ (x^( 2) /2) cos (ln(x ))]_0 ^1 +(1/2) ∫x. sin(ln(x ))dx} := ((−1)/4) −(1/4) Ω (5/4) Ω = ((−1)/4) ⇒ Ω := ((−1)/( 5)) .........■ m.n .................................

$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Solve}\:.......... \\ $$$$\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}.\:{sin}\left(\:{ln}\:\left({x}\:\right)\right){dx}\:\overset{?} {=}\:\frac{−\mathrm{1}}{\:\:\:\mathrm{5}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{solution}.... \\ $$$$\:\:\:\:\:\Omega\::\overset{{i}.{b}.{p}} {=}\left[\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{2}}\:.\:{sin}\left({ln}\left({x}\right)\right)\right]_{\mathrm{0}} ^{\:\mathrm{1}} −\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\mathrm{1}} \:{x}.{cos}\left(\:{ln}\:\left({x}\:\right)\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\::=\:\frac{−\mathrm{1}}{\mathrm{2}}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}.\:{cos}\:\left({ln}\:\left({x}\:\right)\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\::\overset{{i}.{b}.{p}} {=}\:\frac{−\mathrm{1}}{\mathrm{2}}\:\left\{\left[\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{2}}\:{cos}\:\left({ln}\left({x}\:\right)\right)\right]_{\mathrm{0}} ^{\mathrm{1}} +\frac{\mathrm{1}}{\mathrm{2}}\:\int{x}.\:{sin}\left({ln}\left({x}\:\right)\right){dx}\right\} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\::=\:\frac{−\mathrm{1}}{\mathrm{4}}\:−\frac{\mathrm{1}}{\mathrm{4}}\:\Omega \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{4}}\:\Omega\:=\:\frac{−\mathrm{1}}{\mathrm{4}}\:\:\Rightarrow\:\:\:\Omega\::=\:\frac{−\mathrm{1}}{\:\mathrm{5}}\:\:.........\blacksquare\:{m}.{n} \\ $$$$\:\:\:\:.................................\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 152772 Answers: 1 Comments: 2

if ((((x−2))^(1/3) +2))^(1/3) + ((2−((x−2))^(1/3) ))^(1/3) =2 then find the value of (√(198x^4 −868x^3 −229x^2 +200x))

Question Number 152771 Answers: 0 Comments: 2

If f(z) = z sin(z) + ∣z∣^2 , verify if f(z) satisfy cauchy rieman condition

$$\mathrm{If}\:\:\:\:\mathrm{f}\left(\mathrm{z}\right)\:\:\:=\:\:\:\:\mathrm{z}\:\mathrm{sin}\left(\mathrm{z}\right)\:\:\:+\:\:\:\mid\mathrm{z}\mid^{\mathrm{2}} ,\:\:\:\:\:\:\:\mathrm{verify}\:\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{z}\right)\:\:\:\mathrm{satisfy}\:\mathrm{cauchy}\:\mathrm{rieman} \\ $$$$\mathrm{condition} \\ $$

Question Number 152770 Answers: 0 Comments: 1

How to prove that a<b<c ⇒ a+b > c which a,b,c are sides of a triangle ?

$${How}\:\:{to}\:\:{prove}\:\:{that} \\ $$$$\:\:{a}<{b}<{c}\:\:\Rightarrow\:\:{a}+{b}\:>\:{c} \\ $$$${which}\:\:{a},{b},{c}\:\:{are}\:\:{sides}\:\:{of}\:\:{a}\:\:{triangle}\:? \\ $$

Question Number 152769 Answers: 1 Comments: 1