1. Suppose f(x) is a continuous function on r E [a, b]. Prove f(x)dx| < SiIf(x)| dx.2. Let f be a differentiable continuous function on [a, b] and suppose f' is continuous on [a, b]. Prove1| r()S(C)dt = ; (f(b) – S*(@)) .State any theorems or differentiation rules used in your proof. Hint: let F(x) = f²(x).

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1. Suppose f(r) is a continuous function on r E [a, b]. Prove f(x)dx < Slf(x)| dx.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

1. Suppose f(x) is a continuous function on r E [a, b]. Prove f(x)dx| < SiIf(x)| dx.
2. Let f be a differentiable continuous function on [a, b] and suppose f' is continuous on [a, b]. Prove
1
| r()S(C)dt = ; (f(b) – S*(@)) .
State any theorems or differentiation rules used in your proof. Hint: let F(x) = f²(x).

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