- #1
madsmh
- 32
- 2
I am currently working on problem 32-15 in Calculus by Spivak, and in question (b)
in the bottom line there is a relation
[\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]+[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0
But I can only get it to work out if
[\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]-[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0
as this would make sense since
which would make it natural to conclude that the relation above is >0, since the above integral has been shown to be >0.
.. Mads
in the bottom line there is a relation
[\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]+[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0
But I can only get it to work out if
[\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]-[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0
as this would make sense since
\int_a^b \phi_1''(x)\phi_2(x)-\phi_2''(x)\phi_1(x) + \phi_1'(x)\phi_2'(x)-\phi_1'(x)\phi_2'(x) dx = \int_a^b (\phi_1'(x)\phi_2(x))' dx - \int_a^b (\phi_2'(x)\phi_1(x))' dx
which would make it natural to conclude that the relation above is >0, since the above integral has been shown to be >0.
.. Mads
