Friday, October 12, 2018

Single Variable Calculus, Chapter 5, 5.3, Section 5.3, Problem 24

Find the integral 813xdx

Using 2nd Fundamental Theorem of Calculus

baf(x)dx=F(b)F(a), where F is any anti-derivative of f.

Let f(x)=3x or f(x)=(x)13, then


F(x)=x13+113+1+CF(x)=x4343+CF(x)=3x434+C



813xdx=F(8)F(1)813xdx=3(8)434+C[3(1)434+C]813xdx=3[(8)13]44+C34C813xdx=3(2)4434813xdx=3(16)34813xdx=4834813xdx=454 or 813xdx=11.25

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