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04:27{Use of Tech} Riemann sums for larger values of n Complete the following steps for the given function f and interval.
Ζ(π) = 3 βx on [0,4] ; n = 40
(b) Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f and the x-axis on the interval.
Properties of integrals Use only the fact that β«ββ΄ 3π (4 βπ) dπ = 32, and the definitions and properties of integrals, to evaluate the following integrals, if possible.
(b) β«ββ΄ π(π β 4) d(π)
{Use of Tech} Approximating net area The following functions are positive and negative on the given interval.
f(x) = sin 2x on [0,3Ο/4]
(b) Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4.
Working with area functions Consider the function Ζ and the points a, b, and c.
(b) Graph Ζ and A.
Ζ(π) = 1/π ; a = 1 , b = 4 , c = 6
Properties of integrals Consider two functions Ζ and g on [1,6] such that β«ββΆΖ(π) dπ = 10 and β«ββΆg(π) dπ = 5, β«ββΆΖ(π) dπ = 5 , and β«ββ΄g(π) dπ = 2. Evaluate the following integrals.
(b) β«ββΆ (f(π) β g(π)) dπ
The following functions are positive and negative on the given interval.
Ζ(π) = xeβ»Λ£ on [-1,1]
(b) Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n = 4.
