Register to reply

Showing the properties of differentiating an integral

Share this thread:
greswd
#1
Jan18-13, 02:11 PM
greswd's Avatar
P: 147
How do we show that

[tex]\frac{d}{dt}\left[\int\!y\,\mathrm{d} x\right] = y\,\frac{dx}{dt}[/tex]
Phys.Org News Partner Science news on Phys.org
Guidelines for enhancing solar cells using surface plasmon polaritons
Trees and shrubs invading critical grasslands, diminish cattle production
Climate change will threaten fish by drying out Southwest US streams, research predicts
Mark44
#2
Jan18-13, 03:33 PM
Mentor
P: 21,249
Quote Quote by greswd View Post
How do we show that

[tex]\frac{d}{dt}\left[\int\!y\,\mathrm{d} x\right] = y\,\frac{dx}{dt}[/tex]
Is this a homework problem?
HallsofIvy
#3
Jan18-13, 03:56 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,488
Quote Quote by greswd View Post
How do we show that

[tex]\frac{d}{dt}\left[\int\!y\,\mathrm{d} x\right] = y\,\frac{dx}{dt}[/tex]
Are we to assume, here, that y and x are functions of t? If we assume that y is a function of x only (with no "t" that is not in the "x") and x is a function of t, then we an write y(x(t)).

Of course, then [tex]F(x)= \int y dt[/tex] is the function such that dF/dx= y. Given that, we have that [itex]d/dt(\int y dx)= dF/dt= (dF/dx)(dx/dt)= y(x)(dx/dt)[/itex] by the chain rule.

greswd
#4
Jan18-13, 04:07 PM
greswd's Avatar
P: 147
Showing the properties of differentiating an integral

Quote Quote by Mark44 View Post
Is this a homework problem?
Nope. Homework questions are usually standard, and answers are all in the textbooks.
I came up with this problem just out of curiosity.


Anyway, thanks for the solution HallsofIvy
DrewD
#5
Jan18-13, 10:57 PM
P: 446
Quote Quote by greswd View Post
Nope. Homework questions are usually standard, and answers are all in the textbooks.
I wish my textbooks had the answers!
greswd
#6
Jan22-13, 06:57 AM
greswd's Avatar
P: 147
Quote Quote by DrewD View Post
I wish my textbooks had the answers!
not the exact answers, but they all follow the same template


Register to reply

Related Discussions
Differentiating under the integral Calculus & Beyond Homework 1
Differentiating an integral Calculus & Beyond Homework 3
[Linear Algebra] Showing equality via determinant properties Precalculus Mathematics Homework 1
Differentiating an integral Calculus & Beyond Homework 1
Differentiating an Integral Calculus & Beyond Homework 2