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.) [²√8-x² dx, (a) the trapezoidal rule 3.747723 (b) the midpoint rule 3.750364 (c) Simpson's rule 3.749484 X n = 10 W

Evaluate the indefinite integral Note: Any arbitrary constants used must be an upper-case "C".

VT (2x)[sin (2x²)] cos (x2) the correct re-expressed integral in terms of u. Choose and circle one. For the integral dx, suppose we make this substitution: u = x². Determine (A) (B) (C) (D) (E) (F) (G) * sin (u) du cos (u) sin (2u) -du cos (u) None of these sin (2u) -du cos (u) du tan(2u)du tan(u)du|| choices represent a correct integral in terms of u. cos (u)

A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.