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
please solve 413,423
Transcribed Image Text:401.
402.
112
413.
414.
415.
J25+ 16x²
dx
√x²-9
SINIVA
dx
x√4x² - 16
tan
-1
(21) dt
1+4t²
"ttan-¹ (1²)
1+14
(1)
sec
1₁√₁²_4
-4
dt
dt
411.
412.
In the following exercises, compute the antiderivative
using appropriate substitutions, and state its domain.
426.
427.
428.
fsin
sin-¹ tdt
√₁-t²
Sin-
dt
sin-¹1-1²
dt
t(1 + In²t)
COS
Page
-1 (21) dt
√1 - 41²
COS
fe' cos
:-¹ (e¹),
√1-e²t
1
of 7
Chapter 1 | Integration
ZOOM
+
|
![417. [T]
418. [T]
419. [T]
420. [T]
421. [T]
422. [T]
423.
424.
x√x²
425.
√( 2x + 2)√x²
Si
(sinx+xcosx)
1 + x² sin²x
2e-2x
- e
sin
1
√x + x ² x
-1
-dx over [2, 6]
.4
X
-4x
x
2
112, de
ex
√1-e²x
In the following exercises, compute each integral using
appropriate substitutions.
dx over [0, 6]
-dx
2x
dt
t√1 - In²t
dx over [-6, 6]
dx over [0, 2]
-over [0, 2]
-over [-1, 1]
This OpenStax book is available for free at http://cnx.org/content/col11965/1.2
431.
432.
433.
1/2
0
evaluate
.1/2
0
sin(tan-¹t)
1+t²
For A > 0,
Page
t√₁²-1
cos(tan-11)
1 + t²
on [-∞, ∞].
-dt
dt
<
2
evaluate lim I(B),
B→ ∞
-over [1, ∞).
compute I(A) =
A
=[^₁
S
434. For 1 <B<∞o, compute I(B):
>
lim I(A), the area under the graph of
a →∞
=
of 7
dt
-A¹+1²
B
dt
LA
t√₁² - 1
1
the area under the graph of
and
lit
1
1+ t²
and
435. Use the substitution u = √2 cotx and the identity
dx
1 + cot²x = csc² x
csc²x to evaluate
(Hint:
+ cos²x
Multiply the top and bottom of the integrand by csc²x.)
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+
I](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03fd5f25-eded-4046-9c65-9e89b5e28b89%2Fcc4a359c-491b-4ad5-bbf2-8bea41a125ee%2F23thg43_processed.png&w=3840&q=75)
Transcribed Image Text:417. [T]
418. [T]
419. [T]
420. [T]
421. [T]
422. [T]
423.
424.
x√x²
425.
√( 2x + 2)√x²
Si
(sinx+xcosx)
1 + x² sin²x
2e-2x
- e
sin
1
√x + x ² x
-1
-dx over [2, 6]
.4
X
-4x
x
2
112, de
ex
√1-e²x
In the following exercises, compute each integral using
appropriate substitutions.
dx over [0, 6]
-dx
2x
dt
t√1 - In²t
dx over [-6, 6]
dx over [0, 2]
-over [0, 2]
-over [-1, 1]
This OpenStax book is available for free at http://cnx.org/content/col11965/1.2
431.
432.
433.
1/2
0
evaluate
.1/2
0
sin(tan-¹t)
1+t²
For A > 0,
Page
t√₁²-1
cos(tan-11)
1 + t²
on [-∞, ∞].
-dt
dt
<
2
evaluate lim I(B),
B→ ∞
-over [1, ∞).
compute I(A) =
A
=[^₁
S
434. For 1 <B<∞o, compute I(B):
>
lim I(A), the area under the graph of
a →∞
=
of 7
dt
-A¹+1²
B
dt
LA
t√₁² - 1
1
the area under the graph of
and
lit
1
1+ t²
and
435. Use the substitution u = √2 cotx and the identity
dx
1 + cot²x = csc² x
csc²x to evaluate
(Hint:
+ cos²x
Multiply the top and bottom of the integrand by csc²x.)
ZOOM
+
I
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