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Differential Calculus

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9 Jan 2007 15:02:33 IST

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3512

WHO CAN SOLVE THIS?????????

None

Integrate wrt x 1) (sinx)/x and 2) (exponential) e to the power of -x square

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Comments (15)

saket_brutus

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Joined: 25 Dec 2006

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10 Jan 2007 19:26:21 IST

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Hi Kab,

I don't know if u know the answer or not( i have a funny feeling that u do know

- hey; no offence

). But the answer is that these 2 integrals cannot be found( assuming that the 2nd integral is e^{-x^2}).

Cheers.

CyBorG

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11 Jan 2007 16:56:43 IST

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You are right. Most probably they cannot be integrated.
But are you sure??????

amey

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11 Jan 2007 17:09:21 IST

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I am sure that this "CANNOT BE EVALUATED" .
The reason is, not every antiderivative f(x), even when it exists, is expressible in closed form in term of elementary functions such as polynomials, trigo, logarithmic or expo functions.

Manasi

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11 Jan 2007 18:03:37 IST

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I also support the above!!!

CyBorG

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11 Jan 2007 18:12:51 IST

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thanx

saket_brutus

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11 Jan 2007 18:31:43 IST

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Hi Kab,

I'm dead sure.

Cheers.

manini

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14 Jan 2007 21:38:31 IST

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HII KAB, WHEN U KNOW THAT UR QUESTION CAN'T BE EVALUATED THEN WHY U ASK THIS QUESTION?

CyBorG

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15 Jan 2007 16:28:11 IST

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I wasnt sure that they couldnt be evaluated.

manini

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15 Jan 2007 21:57:01 IST

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any body can help me to solve this question

lim(1-cos 4x)/(1-cos 5x)
x->0

manini

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15 Jan 2007 22:00:59 IST

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one more doubt

lim{x(e pow2+x _e pow 2)}/(1-cos x)
x->0

manini

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15 Jan 2007 22:16:53 IST

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hello plz solve my problem

vinu

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15 Jan 2007 22:27:31 IST

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Hi manini,
for ur first Q,
apply L'Hospital 's rule twice;
the ans is 16/25.

vinu

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15 Jan 2007 22:34:24 IST

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For ur 2nd Q,
take e^2 common; u'll be left with ... x(e^x-1)/(1-cosx)
{where ^ means power raised to)
apply L'Hospital 's rule twice again;
the ans is ..2e^2.

manini

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16 Jan 2007 10:49:52 IST

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thank u

CyBorG

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23 Jan 2007 15:27:56 IST

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We know

sinx=x-x³/3!+x⁵/5!+.........

(sinx)/x=1-x²/3!+x⁴/5!+.........

(sinx)dx/x=

(1-x²/3!+x⁴/5!+........)dx

=x-x³/(3)(3!)+x⁵/(5)(5!)+..........+c

So I think its wrong to say(sinx)/x cannot be integrated but the answer is not a finite one.What do you people say?????

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