Tentukan integral tertentu berikut?

Tentukan integral tertentu berikut?

misal

$u = cos(x) \ du = - sin(x) : dx \ - du = sin(x) : dx$

ubah batasnya, substitusi ke u

$frac{pi}{3} to cos( frac{pi}{3} ) = frac{1}{2} \ frac{pi}{4} to : cos( frac{pi}{4} ) = frac{1}{2} sqrt{2}$

maka bentuk integralnya

$int_{ frac{pi}{4} }^{ frac{pi}{3} } frac{ sin(x) }{ { cos}^{2}(x) } dx \ = - int_{ frac{1}{2} sqrt{2} }^{ frac{1}{2} } frac{1}{ {u}^{2} } du \ = - ( frac{1}{ - 2 + 1} {u}^{ - 2 + 1} ) | _{ frac{1}{2} sqrt{2} }^{ frac{1}{2} } \ = frac{1}{u} | _{ frac{1}{2} sqrt{2} }^{ frac{1}{2} } \ = ( frac{1}{ frac{1}{2} } - frac{1}{ frac{1}{2} sqrt{2} } ) \ = 2 - sqrt{2}$