Tertiary Math Blogarooney
Thursday, 9 February 2023
Monday, 17 July 2017
Derivatives and Integration of absolute value functions
The proofs below will use the absolute value functions form as
|f(x)|=\sqrt{f(x)^2}
Proof:
Claim 2: {d\over dx}|f(x)|={f(x)\over |f(x)|}f'(x)
Proof:
Claim 3: \int |x| dx={x|x|\over 2}+c
Proof:
Claim 4: \int x|x| dx={x^2|x|\over 3}+c
Proof:Yes it does generalise,
Claim 5: \int x^n|x| dx={x^{n+1}|x|\over n+2}+c
Proof:
Claim 6: \int |f(x)| dx=??
Proof:
Subscribe to:
Posts (Atom)