Fundemental Theorem of Integral Calculus Suppose f: [a, b] → R is differen- tiable on [a, b] and ƒ' € R(x) on [a,b]. Then [" f'dx = f(b) – ƒ(a). = Define ƒ : [0,2] → R by f(x) = 2x - r² for 0 < x < 1 and f(x) (x-2)² for 1 < x < 2. Prove that f is integrable on [0,2] and find the integral of f over [0,2]. Don not use Theorem 5.10, but rather find the integral by methods similar to those used in the proof of Theorem 5.8.

Fundemental Theorem of Integral Calculus Suppose f: [a, b] → R is differen- tiable on [a, b] and ƒ' € R(x) on [a,b]. Then [" f'dx = f(b) – ƒ(a). = Define ƒ : [0,2] → R by f(x) = 2x - r² for 0 < x < 1 and f(x) (x-2)² for 1 < x < 2. Prove that f is integrable on [0,2] and find the integral of f over [0,2]. Don not use Theorem 5.10, but rather find the integral by methods similar to those used in the proof of Theorem 5.8.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 30EQ

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