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# Definite Integral

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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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#1
+77131
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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

CPhill  Jul 7, 2017
#2
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Thank you very much.

Guest Jul 7, 2017

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