Iff-x-determinant-sec-x-cos-x-sec-2-x-cosec-x-cot-x-cos-2-x-cos-2-x-cosec-2-x-1-cos-2-x-cos-2-x-then-0-pi-2-f-x-dx-

Question Number 59170 by 2772639291927 last updated on 05/May/19

If f (x) = | \begin{matrix} \sec x & \cos x & \sec^{2} x + cosec x \cot x \\ \cos^{2} x & \cos^{2} x & {cosec}^{2} x \\ 1 & \cos^{2} x & \cos^{2} x \end{matrix} |

then \underset{0}{\int^{π / 2}} f (x) d x =

Answered by MJS last updated on 05/May/19

if f (x) = \det (above matrix) :

f (x) = - (\frac{1}{16} \cos 5 x + \frac{5}{16} \cos 3 x - \frac{1}{2} \cos 2 x + \frac{5}{8} \cos x + \frac{1}{2})

F (x) = \int f (x) d x = - (\frac{1}{80} \sin 5 x + \frac{5}{48} \sin 3 x - \frac{1}{4} \sin 2 x + \frac{5}{8} \sin x + \frac{1}{2} x) w

F (\frac{π}{2}) - F (0) = - \frac{π}{2} - \frac{8}{15}

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