# Anirudh's Apostol Calculus Problems thread

1. Jul 22, 2008

### WiFO215

Some time back I made a thread saying I would be buying a calculus book. I ended up buying Apostol as the Indian edition is only 6\$. I have made a thread about this because I can see that there are going to be lots of problems I cannot do and I haven't a solution manual.

1.$$\int$$ (a2 - x2)ndx

2. I am supposed to use integration by parts to do this sum.

3. Using integration by parts,

x(a2 - x2)n + n$$\int$$2x2(a2 - x2)n-1

But he gets a different answer which is

[x(a2 - x2)n + 2a2n$$\int$$(a2 - x2)n-1 dx ]/ 2n+1 + C

Last edited: Jul 22, 2008
2. Jul 22, 2008

### HallsofIvy

Staff Emeritus
HOW did you do the integration by parts? What did you use for u and dv?

3. Jul 22, 2008

### WiFO215

U = (a2- x2)n
V = x

I missed an n in the original equation after the integral. OK. Now what?

4. Jul 22, 2008

### WiFO215

OK. I worked backwards and solved it. But keep this thread open. I shall post any other exercises I have problems with.

5. Jul 28, 2008

### WiFO215

A function f, continuous on the positive real axis, has the property that for all choices of x>0 and y>0, the integral
$$\int$$$$^{xy}_{x}$$f(t)dt
is independent of x (and therefore depends only on y). If f(2) = 2, compute value of integral A(x) = $$\int$$$$^{x}_{1}$$f(t)dt for all x>0