For the function F(t)=ln(t2), let f(t)=F′(t).

Question

Write the integral ∫^b_a f(t)dt and evaluate it with the Fundamental Theorem of Calculus.

∫⁴₁

_dt=

Answer 1

If we take the integral of f(t)=[ln(t^2)]'=[2ln(t)]' with respect to t, we get:

2ln(x) and on the interval 1≤x≤4 we get 2(ln4-ln1)=ln(16)