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Please compute the following definite integral with steps if possible:

Integrate from x=0 to pi/4 [sec x(2tanx - 5secx)]dx. Thank you.

Guest Jul 7, 2017
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2+0 Answers

 #1
avatar+75017 
+1

 

pi/4

∫       [sec x(2tanx - 5secx) ] dx  =

0

 

pi/4                         pi/4

∫    sec x(2tanx)      -       ∫   5 sec^2x  dx  =

0                              0

 

 

  pi/4                                       pi/4

2 ∫    sec x tanx  dx     -       5  ∫   sec^2x   dx  =

  0                                            0

 

             pi/4                               pi/4

2 secx ]                   -      5 tan x ]          =

            0                                    0

 

 

2 [ √2 - 1 ]    -   5 [ 1 - 0 ]  =

 

2√2 - 2 - 5  =

 

2√2  - 7

 

However.....this represents an area  so the correct answer  is 

 

abs ( 2√2  - 7 )  ≈  4.1716  units^2

 

 

 

cool cool cool

CPhill  Jul 7, 2017
 #2
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0

Thank you very much.

Guest Jul 7, 2017

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