Question
Asked Oct 31, 2019
dt =
(c)
(9+t2)3/2
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dt = (c) (9+t2)3/2

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check_circleExpert Solution
Step 1

Given:

9
-dt
3
(9+
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9 -dt 3 (9+

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Step 2

Start by substitution:

Let t 3tan u
differeniate with respect to'u
dt
=3sec2 x
du
dt 3 sec2 xdu
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Let t 3tan u differeniate with respect to'u dt =3sec2 x du dt 3 sec2 xdu

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Step 3

Substitute the value of ‘t’ and...

3sec udu
3 tan u,dt3sec' ucu
(9+(3 tanu)
3sec2 udu
(9+9tan u
3 sec udu
taking 9 common from denominator]
93-(1+tan u)
3sec2 udu
se'u =1+ tan'u]
9
(3-)5(sec'u
3sec udu
91
(3)(secu)
3 sec2 udu
27 sec u
du
9-secu
9 secu
du
secu
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3sec udu 3 tan u,dt3sec' ucu (9+(3 tanu) 3sec2 udu (9+9tan u 3 sec udu taking 9 common from denominator] 93-(1+tan u) 3sec2 udu se'u =1+ tan'u] 9 (3-)5(sec'u 3sec udu 91 (3)(secu) 3 sec2 udu 27 sec u du 9-secu 9 secu du secu

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Tagged in

Math

Calculus