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Magazine Problem 83
Evaluate the integral using area formulas. $$ \int_{-2}^{3}(3-|x|) d x $$
Problem 84
Use averages of values at the left ( \(L\) ) and right ( \(R\) ) endpoints to compute the integrals of the piecewise linear functions with graphs that pass through the given list of points over the indicated intervals. \(\quad\\{(0,0),(2,1),(4,3),(5,0),(6,0),(8,3)\\}\) over [0,8]
Problem 85
Use averages of values at the left ( \(L\) ) and right ( \(R\) ) endpoints to compute the integrals of the piecewise linear functions with graphs that pass through the given list of points over the indicated intervals. \((0,2),(1,0),(3,5),(5,5),(6,2),(8,0)\) over [0,8]
Problem 86
Use averages of values at the left ( \(L\) ) and right ( \(R\) ) endpoints to compute the integrals of the piecewise linear functions with graphs that pass through the given list of points over the indicated intervals. \(\quad\\{(-4,-4),(-2,0),(0,-2),(3,3),(4,3)\\}\) over [-4,4]
Problem 87
Use averages of values at the left ( \(L\) ) and right ( \(R\) ) endpoints to compute the integrals of the piecewise linear functions with graphs that pass through the given list of points over the indicated intervals. \(\\{(-4,0),(-2,2),(0,0),(1,2),(3,2),(4,0)\\}\) over [-4,4]
Problem 88
Suppose that \(\int_{0}^{4} f(x) d x=5\) and \(\int_{0}^{2} f(x) d x=-3,\) and \(\int_{0}^{4} g(x) d x=-1\) and \(\int_{0}^{2} g(x) d x=2 .\) Compute the integrals. $$ \int_{0}^{4}(f(x)+g(x)) d x $$
Problem 89
Suppose that \(\int_{0}^{4} f(x) d x=5\) and \(\int_{0}^{2} f(x) d x=-3,\) and \(\int_{0}^{4} g(x) d x=-1\) and \(\int_{0}^{2} g(x) d x=2 .\) Compute the integrals. $$ \int_{2}^{4}(f(x)+g(x)) d x $$
Problem 90
Suppose that \(\int_{0}^{4} f(x) d x=5\) and \(\int_{0}^{2} f(x) d x=-3,\) and \(\int_{0}^{4} g(x) d x=-1\) and \(\int_{0}^{2} g(x) d x=2 .\) Compute the integrals. $$ \int_{0}^{2}(f(x)-g(x)) d x $$
Problem 91
Suppose that \(\int_{0}^{4} f(x) d x=5\) and \(\int_{0}^{2} f(x) d x=-3,\) and \(\int_{0}^{4} g(x) d x=-1\) and \(\int_{0}^{2} g(x) d x=2 .\) Compute the integrals. $$ \int_{2}^{4}(f(x)-g(x)) d x $$
Problem 92
Suppose that \(\int_{0}^{4} f(x) d x=5\) and \(\int_{0}^{2} f(x) d x=-3,\) and \(\int_{0}^{4} g(x) d x=-1\) and \(\int_{0}^{2} g(x) d x=2 .\) Compute the integrals. $$ \int_{0}^{2}(3 f(x)-4 g(x)) d x $$
