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Title: How to integrate this exponential function? Post by: budsworth on Sep 15, 2012 How to integrate e^(x/3) with an upper limit of ln8 and a lower limit of 0.
Thank you. Title: How to integrate this exponential function? Post by: smithll1 on Sep 15, 2012 Note that d/dx(3*exp(x/3)) = exp(x/3), so we know that F(x) = 3*exp(x/3) is the anti-derivative of our integrand. By the first fundamental theorem of calculus we have
F(ln(8))-F(0) = 3*exp(ln(8)/3) - 3*exp(0/3) = 3*(exp(ln(2))-1) = 3*(2-1) = 3 Title: How to integrate this exponential function? Post by: miggybling on Sep 15, 2012 = 3 e^(x/3) { upper limmit is ln8 , lowr is 0 }
= 3 e^(ln 2) - 3 = 3 x 2 -3 = 3 |