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 times g prime left parenthesis x right parenthesis dx equals Integral 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 following integral.

g(b)
Use the Substitution Formula,f(g(x)). g'(x) dx
f(u) du where g(x) = u, to evaluate the following integral.
g(a)
a
4.
dy
y16y2-
1
2
2
4
dy
y16y2-1
1
2
(Туре
an exact answer in terms of t.)
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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 following integral. g(a) a 4. dy y16y2- 1 2 2 4 dy y16y2-1 1 2 (Туре an exact answer in terms of t.)

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Expert Answer

Step 1

Let us assume y=(sec x)/4

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secx у3 4 dy Or dx secx tanx 4 secx tanx dx Or, dy

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Step 2

When y=-1/2, then x=2pi/3

When y=-...

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When y- 2 V2 When y 4 secx Then 2 V2 secx Then 4 4 4 Or, secx-2 Or, secx=- Or, х3 sec"(-2) Or, Xsec V2 27T Or, x- Зл Or, x= 4

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Tagged in

Math

Calculus