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Integral Calculus

Blazing goIITian

Joined:	13 Aug 2008
Post:	1313

26 Mar 2009 20:34:04 IST

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507

2 Questions .....

None

i got answer fr this as I < 1.57 .... so is it option (D) .... i want 2 verify ...

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aNdRoMeDa

Blazing goIITian

Joined: 10 Sep 2007

Posts: 1319

26 Mar 2009 21:24:33 IST

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for d second one

multiply n divid by sec raise to 6 x

then substitue tanx=t

sec^2xdx=dt

ur int reduces to

t^2dt/(t^3+1)

t^3+1=u

3t^2dt=du

so ur guy basically is

(1/3u^2)du

Madmax

Blazing goIITian

Joined: 24 Dec 2007

Posts: 1111

26 Mar 2009 21:40:17 IST

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First one is not actually an elementary integration problem (wht we're doing is sposedly Elementary Integation!!!!)....one method to do it is using parts and then using This makes it a double integral which can later be calculated

Else U can use the mclaurin series expansion for sinx and then integrate infinite terms!!!

Else, a method my sir had told me for this problem (he said try it in the second yr of college!!!) which I personally have no idea abt......use fourier transforms!! :)

cheers!!

rohit

Blazing goIITian

Joined: 1 Jul 2007

Posts: 301

27 Mar 2009 13:34:25 IST

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the graph of sin(x)/x is given above.it is a decreasing function.

the value of sin(x)/x at x=pi/2 is 2/pi

the area of the trapezium is (1+(2/pi))*(pi/2)/2

area=(pi+2)/4

the area is approximately 1.28

ankit aggarwal

Blazing goIITian

Joined: 10 Feb 2008

Posts: 303

27 Mar 2009 14:17:55 IST

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answer to q1 is [0,3/2]

since in the interval ,

integrating both sides

therefore ans [0,3/2] (pi/2~1.5)

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