Im just a little confused about what the interval would change to? Would this be right for the inner intergral?
Intervals are being changed using u = t2 + s2
Where t = s and t = 0
1/2 \int_{u = s^2}^{u=2s^2} \sqrt{u} du
Using my first method gets very messy. And doesn't work. After the first integration your left with an integration by parts which just gets messier the more you do it. Very stuck.
Homework Statement
Evaluate the integral.
1|0 s|0 ( t . sqrt ( t2 + s2 ) dt dsI hope the way I've written it makes some sort of sense.
The Attempt at a Solution
After getting my head around changing the order of integration I get hit with this question and for some reason am totally...
Homework Statement
Let f be continuous on [a,b] and differentiable on (a,b) Suppose that:
f2(b) f2(a) = b2 - a2:
Prove (using Rolle's theorem) that:( exists x belonging to (a, b) ) ( f'(x)f(x) = x )I just don't know where to start I've done basic proofs with the theorem but only when f(a) =...
Thanks for the feedback it all helps. But still doesn't clear a lot up for me.
For this questions I've proved U+V is a subspace. What your saying is the next step but it doesn't make much sense to me. Can you explain further?
Hey people. I find myself getting through my course but currently with not as much understanding as I would like. We've got to some proofs and i either vaguely understand them or do not know how to prove them.Homework Statement
The first would be to prove the Dimension theorem that.
dimU +...
Cheers!
Right so when i get:
0v = T(v) + T(-v)
i just move the T(v) over because 0v=0?
giving
-T(v) = T(-v)
seems a bit too easy! I've already proved 0x=0 .
Can you explain more about
'You should however explain more clearly why T(v+(-v))=0.'
please =]
1. Suppose V,W are vector spaces over a field F and that T: V ---> W is a linear transformation. Show that for any v belonging to V that T(-v) = -T(v)
2. -T(v) denotes the additive inverse of T(v)
3. I think I'm really overcomplicating it =/ But i have
0v = T( v - v ) = T(v) +...