Functions defined by Integrals

Question

F(x) = ∫[1,x] Ln(t²)dt. Use your calculator to find F '(3)

 

A. 2.197
B. 2.079

C. 1.099

D. 0.693

Answer 1

Remember that taking the derivative of an integral (where the lower limit of the integral is a constant) results in the original function of the upper limit: F'(X) =Ln (X²)

Substitute 3 and you get:  F'(3) = Ln(3²) = Ln(9) = answer A.