4. Yes, more integrals to solve! 1 dx x/lnx tan x dx COS I b) / e* dx a)

Linear Algebra: A Modern Introduction
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Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
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4. Yes, more integrals to solve!
tan x
dx
cos x
1
dx
a)
b)
c)
e dx
5. Show that:
L 1(1 - 2) dz
а)
f(x) dx =
%3D
b) 2
f(x)f'(x) dx = (f(b))² – (f(a))²
Transcribed Image Text:4. Yes, more integrals to solve! tan x dx cos x 1 dx a) b) c) e dx 5. Show that: L 1(1 - 2) dz а) f(x) dx = %3D b) 2 f(x)f'(x) dx = (f(b))² – (f(a))²
1. Compute the following integrals.
1
a) / cos 3z de
b)
dx
VAx +7
(In x)3
c)
xe²²
dx
sin x
1) /
d) ſ e™ sin(e") dx
tan x dx (Hint: tan x =
cos a
arcsin x
dx
VI – x²
i) (2² + 1) /2r³ + 6æ dx
g)
x² + 1
h)
(x2 + 1) /2x3 + 6x dx
2. Find and correct the mistakes in the following “solutions" to these integration problems.
a)
| sin 5x dr; u = 5x, du = 5dx
sin 5x dr = | 5 sin u du = -5 cos u + C = –5 cos 5x +C
cos x
+ sin? x
b)
dr; u = sin x, du = cos xdx
Cos x
du
dx =
1+ sin? x
1+ u²
In |1 + u²|+ C = In |(1 + sin² x)|+C
c) L
(4x + 1)(2x² + x) dx; u = 2x² +x, du = 4x + 1
M-
3
| (4x + 1)(2x² + x)³ dx =
u3 du =
Transcribed Image Text:1. Compute the following integrals. 1 a) / cos 3z de b) dx VAx +7 (In x)3 c) xe²² dx sin x 1) / d) ſ e™ sin(e") dx tan x dx (Hint: tan x = cos a arcsin x dx VI – x² i) (2² + 1) /2r³ + 6æ dx g) x² + 1 h) (x2 + 1) /2x3 + 6x dx 2. Find and correct the mistakes in the following “solutions" to these integration problems. a) | sin 5x dr; u = 5x, du = 5dx sin 5x dr = | 5 sin u du = -5 cos u + C = –5 cos 5x +C cos x + sin? x b) dr; u = sin x, du = cos xdx Cos x du dx = 1+ sin? x 1+ u² In |1 + u²|+ C = In |(1 + sin² x)|+C c) L (4x + 1)(2x² + x) dx; u = 2x² +x, du = 4x + 1 M- 3 | (4x + 1)(2x² + x)³ dx = u3 du =
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