Use the Table of Integrals to evaluate the integral.
⁰∫₋₁ 2t²e-t dt
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
⁴∫₀ e³√ᵗ sin (4t)dt, n=8
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule