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Consider the region bounded by f(x) = x^3 + x + 3 and y = 0...

Consider the region bounded by f(x) = x^3 + x + 3 and y = 0 over [−1, 2].

a) Find the partition of the given interval into n subintervals of equal length. (Write ∆x, x0, x1, x2, · · · , xk, · · · , xn.)

b) Find f(xk), and setup the Riemann sum ∑k=1 f(xk)∆x.

c) Simplify the Riemann sum using the Power Sum Formulas.

d) Find the area of the region by taking limit as n → ∞ of the simplified Riemann sum.

Math   Calculus   
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