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Integrate


[(x^3-7x²+4x-1)]/[(4x²-3x+2)^(0.5)] ?

i have a doubt in the chapter Functions.
What is the meaning of EXTENSION OF A FUNCTION?
and What are ODD and EVEN Functions?
expecting a reply.
Rahul Balakrishnan

I have the following doubts in  kinetic theory of gases :-

 

1. The air density of Mt. Everest is less than that at the sea level. It is found by the mountaineers that for one trip lasting for few hours, the extra oxygen needed by them corresponds to 30000cc at sea level (pressure 1 atm, temperature 27^oC). Assuming that the temperature around Mt. Everest is –73^oC and that the oxygen cylinder has a capacity of 5.2 litres, the pressure at which oxygen should be filled (at site) in the cylinder is

 

1. 1. 3.86 atm
   2. 5.00 atm
   3. 5.77 atm
   4. 1.00 atm

 

 

2. N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of B type is denoted by v² and the mean square of X – component of the velocity of A type is denoted by w², then v²/w² is

 

2. 1. 2
   2. 1
   3. 2/3
   4. 1/2

Evaluate _n→∞lim(1/na+1/na+1+1/na+2+.........+1/nb)

Evaluate  _n->∞lim(0.2^{ln_√5(1/4+1/8+1/16............to n terms)}

Q.   27 identical mercury drops are charged simultaneously to the same potential of 10V. What will be the potential if all the charged  drops are made to combine to form one large drop? (Assume drops to be spherical)

Evaluate _n->∞(lim1.n+2.(n-1)+..........+n.1)/(1²+2²+.......+n²)

Can someone integrate (a²-x²)/x?

1. A square is inscribed in a circle of radius R, a circle is inscribed in this square, then a square in this circle and so on n times. find the limit of the sum of areas of all the squares as   n tends to infinity.
2. Let f(x) be a real value  of function not identically zero, satisfies the relation f(x+y⁷) = f(x) +{f(y)}⁷ for all real x and y and the values of f '(0) is non negative where n(>1) is an odd natural numbers then show that f(1-x)+f(x) =1 .

Can some one integrate

1) xdx/(7x-10-x²)^3/2

2) (cos5x+cos4x)dx/(1-2cos3x)

3)[(x/e)^x+(e/x)^x]logxdx

4)(cos2x.sin4x)dx/{cos⁴x(1+cos²2x)}