bewellplus.gsu.edu
arewab arewab
  • 01-03-2017
  • Mathematics
Answered

If F(x)= integral from 0 to x of square root of (t^3 +1), then F'(2)=

Verified Answer :

LammettHash
LammettHash LammettHash
  • 01-03-2017

By the fundamental theorem of calculus,

\(\displaystyle F'(x)=\frac{\mathrm d}{\mathrm dx}F(x)=\frac{\mathrm d}{\mathrm dx}\int_0^x\sqrt{t^3+1}\,\mathrm dt=\sqrt{x^3+1}\)

which means

\(F'(2)=\sqrt{2^3+1}=\sqrt{8+1}=\sqrt9=3\)

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