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Asked Nov 6, 2019
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the one i circled is the one i am struggling on. i need help with that problem.

8. Use substitution, or a change of variables, to evaluate each definite integral
) V+2
p-
a) 1-2dæ
0
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8. Use substitution, or a change of variables, to evaluate each definite integral ) V+2 p- a) 1-2dæ 0

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Expert Answer

Step 1
The given integral is
-dx
v1+2x2
Let u 12x2 then,
du
(1+2x)
dx
dx
= 4x
du
dx
4x
=
If x 1 then the upper limit is u 1+2(1) 3
If x 0 then the lower limit is u = 1+2 (0) = 1
help_outline

Image Transcriptionclose

The given integral is -dx v1+2x2 Let u 12x2 then, du (1+2x) dx dx = 4x du dx 4x = If x 1 then the upper limit is u 1+2(1) 3 If x 0 then the lower limit is u = 1+2 (0) = 1

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Step 2
Find the value of the integral as follows
3 х du
х
Vu 4x
V1+2x2
1
3
и
_
13
1
и
=_
1
1
2
1
1u
2
1
2u2
4
help_outline

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Find the value of the integral as follows 3 х du х Vu 4x V1+2x2 1 3 и _ 13 1 и =_ 1 1 2 1 1u 2 1 2u2 4

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