Please compute the following definite integral with steps if possible:
Integrate from x=0 to pi/4 [sec x(2tanx - 5secx)]dx. Thank you.
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