For the function F(t)=et2

Question

, let f(t)=F′(t). Write the integral ∫^b_a f(t)dt and evaluate it with the Fundamental Theorem of Calculus.
∫^3_0=
dt=

Answer 1

f(t) = 2tet2

Using the Fundamental Theorem of Calculus, we have:

∫^b_a f(t)dt = F(b) - F(a)

Plugging in the values of a and b, we get:

∫^3_0 f(t)dt = F(3) - F(0)

F(t) = et2

F(3) = e(3)2
F(0) = e(0)2 = 1

∫^3_0 f(t)dt = F(3) - F(0) = e(3)2 - 1 ≈ 19.0857.