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...
Related questions
Question
Solve v. from the letter b section. using the FTC(fundamental theorem of calculus)
![(a) Sketch the boundary and shade the region of integration indicated by the integral. Com-
pute the area using geometry, not the FTC.
i. f³ 5 dx
ii. ³₂ (2x + 4) dx
(b) Evaluate each of the following integrals using the FTC. Look carefully at the intervals
and functions to decide an appropriate approach before you start.
6x³/2-4x¹/2
√4/9
vi. f(x5 + 3x³ - 10x)dx
vii. f(x5 + 3x³ - 10x)dx
i. f10 5x² dx
ii. _3²(x+4) dx
/2
iii. f/² sin(x) dx
iv. ST/6 (sec²(x)) dx
π/6
iii. So √25 - x² dx
iv. ²₁ (5-x+x) dx
V.
CT
da
dx
(c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find
f(x)dx.
(d) Concept Check: Suppose that f(x) is an odd function with fo f(x) dx = 11. Find
1³3 f(x) dx.
-3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9372b6fe-9d83-4cc3-b9b6-3000d02c5781%2Fc30adda3-9161-47a8-bc14-5f88b7396bd5%2Feevxqf9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Sketch the boundary and shade the region of integration indicated by the integral. Com-
pute the area using geometry, not the FTC.
i. f³ 5 dx
ii. ³₂ (2x + 4) dx
(b) Evaluate each of the following integrals using the FTC. Look carefully at the intervals
and functions to decide an appropriate approach before you start.
6x³/2-4x¹/2
√4/9
vi. f(x5 + 3x³ - 10x)dx
vii. f(x5 + 3x³ - 10x)dx
i. f10 5x² dx
ii. _3²(x+4) dx
/2
iii. f/² sin(x) dx
iv. ST/6 (sec²(x)) dx
π/6
iii. So √25 - x² dx
iv. ²₁ (5-x+x) dx
V.
CT
da
dx
(c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find
f(x)dx.
(d) Concept Check: Suppose that f(x) is an odd function with fo f(x) dx = 11. Find
1³3 f(x) dx.
-3
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