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Question Number 142255 by gsk2684 last updated on 28/May/21
find the value of ∫_0 ^1 (√(x^4 −5x^2 +4)) dx?  solution please.
findthevalueof01x45x2+4dx?solutionplease.
Answered by mindispower last updated on 28/May/21
by part=[x(√(x^4 −5x^2 +4))]_0 ^1 −∫_0 ^1 ((2x^4 −5x^2 )/( (√(x^4 −5x^2 +4))))dx  =−2∫_0 ^1 (√(x^4 −5x^2 +4))+∫_0 ^1 ((−5x^2 +8)/( (√(x^4 −5x^2 +4))))dx  ∫_0 ^1 (√(x^4 +5x^2 +4))dx=(1/3)∫_0 ^1 ((−5x^2 +8)/( (√(x^4 −5x^2 +4))))dx  x^4 −5x^2 +4=(1−x^2 )(4−x^2 )  (1/3)∫_0 ^1 ((5(4−x^2 )−12)/( (√(x^2 −5x^2 +4))))dx  =(5/3)∫_0 ^1 ((√(4−x^2 ))/( (√(1−x^2 ))))dx−4∫_0 ^1 (dx/( (√((1−x^2 )(4−x^2 )))))  =((10)/3)∫_0 ^1 ((√(1−(1/4)x^2 ))/( (√(1−x^2 )))) −2∫_0 ^1 (dx/( (√((1−x^2 )(1−(x^2 /4))))))  E(k^2 )=∫_0 ^1 ((√(1−k^2 x^2 ))/( (√(1−x^2 ))))dx 2nd eleptic integral   K(k^2 )=∫_0 ^1 (dx/( (√(1−x^2 .(√(1−k^2 x^2 ))))))  1 st kind eleptic integral  we Get∫_0 ^1 (dx/( (√(x^4 −5x^2 +4))))= ((10)/3)E((1/4))−2K((1/4))
bypart=[xx45x2+4]01012x45x2x45x2+4dx=201x45x2+4+015x2+8x45x2+4dx01x4+5x2+4dx=13015x2+8x45x2+4dxx45x2+4=(1x2)(4x2)13015(4x2)12x25x2+4dx=53014x21x2dx401dx(1x2)(4x2)=10301114x21x2201dx(1x2)(1x24)E(k2)=011k2x21x2dx2ndelepticintegralK(k2)=01dx1x2.1k2x21stkindelepticintegralweGet01dxx45x2+4=103E(14)2K(14)
Commented by MJS_new last updated on 29/May/21
great!
great!
Commented by mindispower last updated on 29/May/21
thanx sir
thanxsir
Commented by gsk2684 last updated on 31/May/21
thank you
thankyou

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