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Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F(x) and G(x) are antiderivatives of f(x) and g(x) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, [cf(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [[f(x) + g(x)] dx = F(x) + G(x) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [{f(x) − g(x)] dx = F(x) − G(x) + C. - da - x7+1 r+1 » / 20² NOTE: Enter the exact answer. The power rule: x" dx = 7 +]dy = SH - √5 + + C, r = -1. +C

Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F(x) and G(x) are antiderivatives of f(x) and g(x) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, [cf(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [[f(x) + g(x)] dx = F(x) + G(x) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [{f(x) − g(x)] dx = F(x) − G(x) + C. - da - x7+1 r+1 » / 20² NOTE: Enter the exact answer. The power rule: x" dx = 7 +]dy = SH - √5 + + C, r = -1. +C

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 22E: Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and...
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Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F(x) and G(x) are antiderivatives of f(x) and g(x) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, [cf(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [{f(x) + + g(x)] dx = F(x) + G(x) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [[{f(x) — 9(x)] da = F(x) − G(x) + C. x²+1 r+1 [₂ NOTE: Enter the exact answer. The power rule: S# -* x dx = 7 3y + dy = √y + C,r-1. +C
Transcribed Image Text:Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose that F(x) and G(x) are antiderivatives of f(x) and g(x) respectively, and that c is a constant. Then: (a) A constant factor can be moved through an integral sign; that is, [cf(x) dx = cF(x) + C. (b) An antiderivative of a sum is the sum of the antiderivatives; that is, [{f(x) + + g(x)] dx = F(x) + G(x) + C. (c) An antiderivative of a difference is the difference of the antiderivatives; that is, [[{f(x) — 9(x)] da = F(x) − G(x) + C. x²+1 r+1 [₂ NOTE: Enter the exact answer. The power rule: S# -* x dx = 7 3y + dy = √y + C,r-1. +C
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