Chain Rule question
- Thread starter Joeman
- Start date
i would probably know how to do that, had i not dropped my current calculus class. so the best i can do is say check for yourself!!!!!!
http://integrals.wolfram.com/
the integrator .. works nice
http://integrals.wolfram.com/
the integrator .. works nice
<i>1. Do you guys know how to integrate
y(x) = 2x / (x^2 + 3) ???</i>
Yes.
Put u = x^2 + 3
Then du/dx = 2x
Integral (2x / (x^2 +3)) dx
= Integral ((du/dx) / u) dx
= Integral (1/u) du
= ln u + c
= ln (x^2 + 3) + c
<i>2. The integral of e^(x^2) is 1/(2x)*e^(x^2) correct?</i>
No. You can see that's wrong by differentiating your answer.
y(x) = 2x / (x^2 + 3) ???</i>
Yes.
Put u = x^2 + 3
Then du/dx = 2x
Integral (2x / (x^2 +3)) dx
= Integral ((du/dx) / u) dx
= Integral (1/u) du
= ln u + c
= ln (x^2 + 3) + c
<i>2. The integral of e^(x^2) is 1/(2x)*e^(x^2) correct?</i>
No. You can see that's wrong by differentiating your answer.
mathematica says the answer is Log(3+x^2)
Log in mathematica is ln i believe, from the version i used at school
Log in mathematica is ln i believe, from the version i used at school
On Radioactive Waves,
Indeed it is, mostly log = ln, and log10 equals just what it says (the inverse function of powers of ten). Some books/courses prefer the distinct notation log for log10 and ln for the inverse of the exponential.
The lesson is: always check the convention used in a text before reading the formula's. Something which goes far beyond ln/log confusion
Bye!
Crisp
Indeed it is, mostly log = ln, and log10 equals just what it says (the inverse function of powers of ten). Some books/courses prefer the distinct notation log for log10 and ln for the inverse of the exponential.
The lesson is: always check the convention used in a text before reading the formula's. Something which goes far beyond ln/log confusion
Bye!
Crisp
~The_Chosen~
Registered Senior Member
I advise you to buy Micheal Kelley's Mastering the AP Calculus AB + BC by ARCO
It's the best calculus prep book out there. It'll help you to understand everything - limits, integrals, differentiation, to slope/field solutions graphs.
It's the best calculus prep book out there. It'll help you to understand everything - limits, integrals, differentiation, to slope/field solutions graphs.