Question
Asked Jul 8, 2019
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Use the substitution formula

Integral from a to b f left parenthesis g left parenthesis x right parenthesis right parenthesis g prime left parenthesis x right parenthesis dx

equalsIntegral from g left parenthesis a right parenthesis to g left parenthesis b right parenthesis f left parenthesis u right parenthesis du

 

where

​g(x)equals
u

to evaluate the integral below.

g(b)
Use the substitution formula f(g(x))g'(x)dx
f(u)du where g(x) = u to evaluate the integral below
g(a)
a
612
2 ds
V144 s2
0
612
2Tt
2 ds
12
V144 2
-S
0
(Туре
as needed.)
an exact answer,
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g(b) Use the substitution formula f(g(x))g'(x)dx f(u)du where g(x) = u to evaluate the integral below g(a) a 612 2 ds V144 s2 0 612 2Tt 2 ds 12 V144 2 -S 0 (Туре as needed.) an exact answer,

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Expert Answer

Step 1

Obtain the value of the integral as follows.

62
The given integral is J J144- s2
2ds
(1)
Let s 12 sin u then ds 12 cosudu
1
1
144-(12sin u144-144(sin* u)
1
12/1-sin2u
1
12/cos u
1
12 cosu
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62 The given integral is J J144- s2 2ds (1) Let s 12 sin u then ds 12 cosudu 1 1 144-(12sin u144-144(sin* u) 1 12/1-sin2u 1 12/cos u 1 12 cosu

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Step 2

Substitute the obtained values in equation (1),

62
62
12 cosudu
2ds
-2/
V144-2
12 cosu
0
642
-2 du
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62 62 12 cosudu 2ds -2/ V144-2 12 cosu 0 642 -2 du

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Step 3

Compute the limit ...

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Calculus

Integration

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