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Integral Calculus

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28 Oct 2007 13:34:36 IST

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can u integrate this for few points??????????????

None

integrate the following with respect to x

{1} x⁴

________

(x-1)(x+1)²

^{2}x³

^{____________________}

(x-1)(x-2)

note: in this type degree of numerator is greater than degree of denominator

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Comments (5)

venkat v.t

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Joined: 7 Aug 2007

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28 Oct 2007 13:46:27 IST

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Just divide by using division of polynomials and reduce the degree
of numerator than that of denominator .Then integrate.

'',' Off to a nu start!!

Blazing goIITian

Joined: 13 Jan 2007

Posts: 1289

28 Oct 2007 13:46:47 IST

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in above type try to make numerator a multiple of denominator & the n break the numerator & partial fraction.......okkk....for example:-

2nd qn. add & subtract 1 in num....so u will get

x^3 -1 + 1
break the numeraotr at + 1

u will get

(x-1)(x^2 + x+1)

x-1 cancels out............so we get

x^2 + x+1/x-2

now try to make the num. again the whole square of x-2 so for dat add & subtract 5x & 3 & break the num.. agin..
u will get

x-2 )^2 + 5x - 3/x-2
breaking we get
x-2 + integral of 5x-3/x-2...& now i think u must hv done linear/linera type......

HOPE THIS HELPPSSS!!!!!!

angelH

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28 Oct 2007 14:12:26 IST

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the solution of this example if done by PARTIAL FRACTIONS can u try

'',' Off to a nu start!!

Blazing goIITian

Joined: 13 Jan 2007

Posts: 1289

28 Oct 2007 14:31:56 IST

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my dear,partial fraction is done only ,i think, when degree of num. is less then dat of denom.

so why to use it here.......

venkat_tatolu & i hv given u methods so follow them!!!!!

hope u understand!!!!!

Neeraj Agarwal

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Joined: 22 Jan 2007

Posts: 2039

28 Oct 2007 21:27:38 IST

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divide the numerator and denomenator (i hope u know how to do that!)

then write numerator as divisor x quotient + remainder...

then u can use partial fractions...

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