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divalli_oct07

1) _{[ o]}

^{[ n]} {x} dx = n/2 where {x} means fractional part of x (n belongs to

integers)

2)_{[ o]}

^{[n ]} [x] dx = n (n-1)/2 ( n belongs to integers)

3) _{[ a]}

^{[ b]} [x] dx = 1/2( [b] - [a] ) ( [b] +[a] - 1) + [b]{b} - [a]{a} ( a , b are not

integers)

4)_{[a ]}

^{[b ]} modulus (x)/x dx = modulus(b) - modulus (a)

5)_{[ 0]}

^{[ ]} dx / (x+^{[ 2]}

x² +1)^{n =} n/n² - 1

6)_{[o ]}

^{[ /2]} sinⁿx / sinⁿx + cosⁿx dx =

/4

the above formula is valid for( tan and cot), (sec and cosec) also

7)_{[ ]}

^{[ ]} e^x xⁿdx = e^x(xⁿ-nx^n-1 + n*n-1x^n-2 -....const)

for example:-

e^xx³ dx =e^x(x³ - 3x² +6x - 6)

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