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Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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57 ANTIDERIVATIVES INTEGRATION AS: 1. A REVERSE OF DIFFERENTIATION ANTIDERIVATIVE 4x² + c Example 1: F(x) F'(x) = 12x² 12x dx 4x + c BOE 4x + C 12x² If f'(x) = 3x² + e² + 2 and f(0) = -4, find f(x). f'(x) = 3x² + ²x + 2 f(x) ff'(x) dx = f(3x² + ²x + 2) dx e²x x³ + + 2x + c 0 + -4 => + 2(0) + c = -4 f(0) = + + 0 + C = -4 C = -4 e2x = x³ + + 2x - -4/2/2 2 + c where c is a constant Find g (t) if fg (t)dt = √4-P Example 2: Solution: Example 3: Solution: f(x) ANTIDERIVATIVES 0 e²(0) 2 1 2 Let y = (4-²) + c dy g (t) = dt -(4-²)*(-21) = = (4-1)/² 223 I con ST ANTI Exam Solut
Transcribed Image Text:57 ANTIDERIVATIVES INTEGRATION AS: 1. A REVERSE OF DIFFERENTIATION ANTIDERIVATIVE 4x² + c Example 1: F(x) F'(x) = 12x² 12x dx 4x + c BOE 4x + C 12x² If f'(x) = 3x² + e² + 2 and f(0) = -4, find f(x). f'(x) = 3x² + ²x + 2 f(x) ff'(x) dx = f(3x² + ²x + 2) dx e²x x³ + + 2x + c 0 + -4 => + 2(0) + c = -4 f(0) = + + 0 + C = -4 C = -4 e2x = x³ + + 2x - -4/2/2 2 + c where c is a constant Find g (t) if fg (t)dt = √4-P Example 2: Solution: Example 3: Solution: f(x) ANTIDERIVATIVES 0 e²(0) 2 1 2 Let y = (4-²) + c dy g (t) = dt -(4-²)*(-21) = = (4-1)/² 223 I con ST ANTI Exam Solut
57 ANTIDERIVATIVES TUTORIAL 57 9 + ²* + x³ and f(1) = 1. Given f'(x) = find f(x). 2. \If w'(x) = 4x³ + 3x² + 4x and w(1) = 12, find w(x). 1 3. If f'(x) = + ex and f(0) = 1, find f (x). X + 1 Find a function F such that F'(x) = x - sin 3x and F (0) = - 5. Find the antiderivative F(x) of f(x) = 3x² + 2 satisfying FC 1 dy 1 Given y = . Hence, evaluate find (3x - 1)³₁ dx (3x- Hence, evaluate (2 – 3x)², (2 Given y swers: f(x) = w (x) = f(x) = In x + x² + x³ + 2x² In (x + 1) + 3x 4x e 4 2 find 314 dy dx -1
Transcribed Image Text:57 ANTIDERIVATIVES TUTORIAL 57 9 + ²* + x³ and f(1) = 1. Given f'(x) = find f(x). 2. \If w'(x) = 4x³ + 3x² + 4x and w(1) = 12, find w(x). 1 3. If f'(x) = + ex and f(0) = 1, find f (x). X + 1 Find a function F such that F'(x) = x - sin 3x and F (0) = - 5. Find the antiderivative F(x) of f(x) = 3x² + 2 satisfying FC 1 dy 1 Given y = . Hence, evaluate find (3x - 1)³₁ dx (3x- Hence, evaluate (2 – 3x)², (2 Given y swers: f(x) = w (x) = f(x) = In x + x² + x³ + 2x² In (x + 1) + 3x 4x e 4 2 find 314 dy dx -1
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