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Integral Calculus

Hot goIITian

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19 Jul 2009 10:40:14 IST

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can u tell me how to get a better hold of integration of definite greatest integer function eg-to f

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can u tell me how to get a better hold of integration of definite greatest integer functioneg-to find integration of [x^2] within limits (-1,1.7)plsssssssssssssssi need helppls temme any website or giv any information cos these functions r really troubling me!!!!!!!!!!!!!!

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swapneal.........

Blazing goIITian

Joined: 27 Apr 2009

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19 Jul 2009 10:42:51 IST

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intigeration is abt practise all , the more u solve question more u will have control on integration. first try to learn formulae by applying that in problem

Abhinav... new lyf, new hopes, new ambitions

Hot goIITian

Joined: 31 Dec 2007

Posts: 188

19 Jul 2009 11:18:36 IST

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try arihant's integral calculus...i think its d best der is....apart from teaching different concepts, it helps u grasp d concepts...der r many solved questions of d type u asked in dat buk....else u can also hav a look at d solved problems in integral calculus from TataMcGraw Hill's...and do remember dat calculus(in fact, entire maths) is all abt practise...

Abhinav... new lyf, new hopes, new ambitions

Hot goIITian

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19 Jul 2009 11:18:37 IST

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Sujit

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19 Jul 2009 11:21:15 IST

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SOME USEFUL SHORTCUTS FOR FUNCTIONS :

1.   $\int_{a}^{b}$ [ x ]dx = { (b-a)(b+a-1) }/2
                    = (upper limit - lower limit)(upper limit + lower limit - 1) / 2
             where [.] denotes greatest integer value function a,b $\in$ I
2.    $\int_{a}^{b}$ [x]dx = n(n-1)/2      where a = 0 & b = n
         where [.] denotes the greatest integer value function. n $\in$ I
3.    $\int_{a}^{b}$ {x}dx = n/2            where a = 0 & b = n
         where {.} denotes fractional function. n $\in$ I
4.    $\int_{a}^{b}$ [x]dx = [n]*( (n+{n}-1)/2 )      where a = 0 & b = n
         where [.] denotes the greatest integer value function. n $\in$ R
5.   $\int_{a}^{b}$ {x}dx = n^2/2 - [n]( (n+{n}-1)/2 )   where a = 0 & b = n
         where {.} denotes the fractional function. n $\in$ R
6. $\int_{a}^{b}$ {x}dx = (b-a)/2
          where {.}denotes fractinol function. a,b $\in$ I
7.   $\int_{a}^{b}$ [kx]dx = nk(nk-1)/2k      where a = 0 & b= n
         where [.] denotes greatest integer value function.   n,k $\in$ I
8. $\int_{a}^{b}$ [x^2] dx= -(1 + 2^1/2 + 3^1/2 + ...(n^2-1)^1/2) + (n^2-1)n where a= 0 & b= n
         where [.] denotes the greatest integer value function. n $\in$ I
9. $\int_{a}^{b}$ [x^k]dx= -(1 + 2^1/k + 3^1/k +.... (n^k-1)^1/k )+ (n^k-1)n where a= 0 & b= n
         where [.] denotes greatest integer value function. n,k $\in$ I
10. $\int_{a}^{b}$ [sinkx]dx = - $\pi$ /k         where a = 0 & b = 2 $\pi$ /k
         where [.] denotes the greatest integer value function. k $\in$ I
11.   $\int_{a}^{b}$ [coskx]dx = - $\pi$ /k        where a = 0 & b = 2 $\pi$ /k
         where [.] denotes greatest integer value function. k $\in$ I
12. $\int_{a}^{b}$ [x/k]dx = pn - (p(p+1)k)/2     where a = 0 & b= n
        where p = [n/k], [.] denotes greatest integer function & n,k $\in$ I
13.   $\int_{a}^{b}$ {kx}dx = n/2           where a = 0 & b = n
       where {.} denotes fractional function. n $\in$ I
14.   $\int_{a}^{b}$ {x/k}dx = n^2/2k - pn + (p(p+1)k)/2     where a = 0 & b = n
       where p = [n/k], {.} denotes fractional function & n,k $\in$ I

Sparkling kid

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22 Jul 2009 13:08:56 IST

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thanx a lot yeah ..dese are really goin to help me!!!!!!!!!!!!!!

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