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07:33Properties 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)
Matching functions with area functions Match the functions Ζ, whose graphs are given in aβ d, with the area functions A (π) = β«βΛ£ Ζ(t) dt, whose graphs are given in AβD.
{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
{Use of Tech} Approximating definite integrals with a calculator Consider the following definite integrals.
(b) Evaluate each sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral.
β«βΒΉ cos β»ΒΉ π dπ
