Fill in the following table of values for I(x)=∫^x_0√(t^4+1)dt.
(a) I(0)=0
(b) I(0.5)=0.503
(c) I(1)=1.08943
(d) I(1.5)=
(e) I(2)=
To fill in the table for (d) and (e), we need to evaluate the definite integral for those values of x:
(d) I(1.5) = ∫^1.5_0 √(t^4+1) dt ≈ 1.703
(e) I(2) = ∫^2_0 √(t^4+1) dt ≈ 2.663
Note that these values are approximations, as we used numerical methods to evaluate the definite integrals.