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Integral Calculus

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29 Oct 2007 20:56:39 IST

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Some very exclusive and extremely tough Integration problems

None

Q.1 Let f(x) x0 be a non -ve continuous function. If f `(x).cosx f(x).sinx x0
,then the value of f(5/3) = .....
a)e^{-1/ 3}      b) 3+1      c) 3-1    d)0
                        2              2

Q.2 The natural no. n5 for which I_n=e^x(x-1)ⁿ.dx = 16-6e is.......
a) 1       b)2         c)3         d)4

Please help me how to solve these two question...
Thnks..

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Comments (6)

Ramya Hegde

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1 Nov 2007 03:51:17 IST

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Hey for the second question, there might be limits included for the integral. Or are u sure this is the complete question??

Anshuman Bhujabal

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1 Nov 2007 05:58:54 IST

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Yes probably u want to ask _[0]^[1] e^x(x-1)ⁿdx

When u integrate it by parts,u would get

[e^x(x-1)ⁿ- e^xn(x-1)^n-1 - e^xn(n-1)(x-1)^n-2 ......]₀¹

So a term will come -n! e + k where k is constant

Given integral was 16 - 6e

So n! = 6

So n=3 for sure

Please rate ......

shivram kashyap

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1 Nov 2007 18:41:30 IST

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f ' (x)cosx - f(x)sinx<=0

d(f(x)cosx)<=0

F(x)=f(x)cosx is decreasing

5pi/3=2pi-pi/3>pi/2

F(5pi/3)<=F(pi/2)

f(5pi/3)cos5pi/3<=0 (cospi/2=0)

f(5pi/3)*(1/2)<=0

f is always>=0

f(5pi/3)=0 is the reqd solution

please rate if u liked it

Niteesh Mehra

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4 Nov 2007 17:44:38 IST

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both answers are wrong...answer to the 1 is c and 2 ka i myself dunoo but the question is correct...

raymont cherian

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4 Nov 2007 22:47:42 IST

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the second question has missing limits cuz as u urself can c .. it is independent of x which can happen only when it is a DI

astrojith

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8 Nov 2007 19:59:30 IST

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Can anyone post a detailed solution for the 1st question ?

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