45. Explain why or why not Determine whether the ments are true and give an explanation or counterexample. a. If m is a positive integer, then b. If m is a positive integer, then 2m+1 cos² x dx = 0. sin" x dx = 0.
45. Explain why or why not Determine whether the ments are true and give an explanation or counterexample. a. If m is a positive integer, then b. If m is a positive integer, then 2m+1 cos² x dx = 0. sin" x dx = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
help with problem 45 both a and b part, please show work on paper. Thank you.
![33.
35.
37.
39.
41.
43.
/
tan x sec³ x dx
/
tan³ 4x dx
[s
sec² x tan¹/2 x dx
csc4 x
S
cot² x
5.
#/3
TT/6
dx
sec 0 de
cot³ 0 de
34.
36.
38.
40.
42.
44.
Vtan x secx dx
sec² x
tan³ x
/
sec-²x tan³ x dx
[s
10
csc ¹0 x cot x dx
[
Stan
dx
tan³ 0 sec¹ 0 de
π/4
S
46. Use a change of variables to prove that
cotx dx = ln \sin x + C.
tan³ 0 sec² 0 de
Further Explorations
45. Explain why or why not Determine whether the following state-
ments are true and give an explanation or counterexample.
2m+1
a. If m is a positive integer, then
b. If m is a positive integer, then
cost x dx = 0.
sin" x dx = 0.
46-47. Integrals of cot x and csc x
47. Prove that fcscx dx = -ln |csc x + cotx + C. (Hint: See the
proof of Theorem 8.1.)
y
48. Comparing areas The region R₁ is bounded by the graph of
= tan x and the x-axis on the interval [0, π/3]. The region R₂
is bounded by the graph of y= sec x and the x-axis on the inter-
val [0, π/6]. Which region has the greater area?
49. Region between curves Find the area of the region bounded by
the graphs of y = tan x and y = secx on the interval [0, π/4].
50-57. Additional integrals Evaluate the following integrals.
6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5222c9e-84ca-49ca-a26b-1a6cb57ce931%2Fb0c94104-86b9-44d0-b9d3-b80be603dc5d%2Fn1opwyc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:33.
35.
37.
39.
41.
43.
/
tan x sec³ x dx
/
tan³ 4x dx
[s
sec² x tan¹/2 x dx
csc4 x
S
cot² x
5.
#/3
TT/6
dx
sec 0 de
cot³ 0 de
34.
36.
38.
40.
42.
44.
Vtan x secx dx
sec² x
tan³ x
/
sec-²x tan³ x dx
[s
10
csc ¹0 x cot x dx
[
Stan
dx
tan³ 0 sec¹ 0 de
π/4
S
46. Use a change of variables to prove that
cotx dx = ln \sin x + C.
tan³ 0 sec² 0 de
Further Explorations
45. Explain why or why not Determine whether the following state-
ments are true and give an explanation or counterexample.
2m+1
a. If m is a positive integer, then
b. If m is a positive integer, then
cost x dx = 0.
sin" x dx = 0.
46-47. Integrals of cot x and csc x
47. Prove that fcscx dx = -ln |csc x + cotx + C. (Hint: See the
proof of Theorem 8.1.)
y
48. Comparing areas The region R₁ is bounded by the graph of
= tan x and the x-axis on the interval [0, π/3]. The region R₂
is bounded by the graph of y= sec x and the x-axis on the inter-
val [0, π/6]. Which region has the greater area?
49. Region between curves Find the area of the region bounded by
the graphs of y = tan x and y = secx on the interval [0, π/4].
50-57. Additional integrals Evaluate the following integrals.
6
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