answer part b and part c d3dThe following integral may be evaluated by using integration by parts.Notes:powers can be entered using ^A• to divide, use /duThe product -5 In(4x) must be written in the form ududu duDetermine u, and ub)Apply the integration by parts formula:16=V=In(4x)Judrfudr =II-5x-5 ln(4x) drUV>>4=-S-S1/x-5dzdz c)Hence write down the indefinite integral:-5 ln (42) dr.(Don't forget the constant of integration as this is an indefinite integral.)-5x 1n(4x) +5x+c -5x ln(4x) + 5x+c x

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3 B d The following integral may be evaluated by using integration by parts. Notes: • powers can be entered using ^ A • to divide, use / The product-5 In(4x) must be written in the form u Determine u, and u du du dz U= V= - 5 In(42) dz in(4x) -5x << 11 II 1/X -5

3 B d The following integral may be evaluated by using integration by parts. Notes: • powers can be entered using ^ A • to divide, use / The product-5 In(4x) must be written in the form u Determine u, and u du du dz U= V= - 5 In(42) dz in(4x) -5x << 11 II 1/X -5

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.3: Area And The Definite Integral

Problem 1E: Explain the difference between an indefinite integral and a definite integral.

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Question

answer part b and part c

d
3
d
The following integral may be evaluated by using integration by parts.
Notes:
powers can be entered using ^
A
• to divide, use /
du
The product -5 In(4x) must be written in the form u
du
du du
Determine u, and u
b)
Apply the integration by parts formula:
16=
V=
In(4x)
Judr
fudr =
II
-5x
-5 ln(4x) dr
UV
>>
4=
-S
-S
1/x
-5
dz
dz

c)
Hence write down the indefinite integral:
-5 ln (42) dr.
(Don't forget the constant of integration as this is an indefinite integral.)
-5x 1n(4x) +5x+c -5x ln(4x) + 5x+c x

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