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Interview Question for Quantitative Analyst at Citi:
Nov 12, 2011
Derive "uv" integral rule from any differentiation identity you remember. You can use only "basic" identities and no "advanced" calculus in your derivation.
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2 of 2 people found this helpful
Jan 17, 2012
Not sure, but...
Let u and v be functions of x. Start with product rule of differentiation:
d(u*v)/dx= u*(dv/dx) + v*(du/dx)
Multiply both sides by dx:
d(u*v) = u*dv + v*du
Integrate:
u*v = integral(u*dv) + integral(v*du)
Rearrange to get formula for integration by parts:
integral(u*dv) = u*v - integral(v*du)
Let u and v be functions of x. Start with product rule of differentiation:
d(u*v)/dx= u*(dv/dx) + v*(du/dx)
Multiply both sides by dx:
d(u*v) = u*dv + v*du
Integrate:
u*v = integral(u*dv) + integral(v*du)
Rearrange to get formula for integration by parts:
integral(u*dv) = u*v - integral(v*du)
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