Cho tích phân \(\int\limits_{0}^{\frac{\pi }{2}}{\left( 4x-1+\cos x \right)\text{d}x}=\pi \left( \frac{\pi }{a}-\frac{1}{b} \right)+c\), \(\left( a,b,c\in \mathbb{Q} \right)\). Tín...

* Hướng dẫn giải

\(\int\limits_0^{\frac{\pi }{2}} {\left( {4x - 1 + \cos x} \right){\rm{d}}x}  = \left. {\left( {2{x^2} - x + \sin x} \right)} \right|_0^{\frac{\pi }{2}} = \pi \left( {\frac{\pi }{2} - \frac{1}{2}} \right) + 1\)

Suy ra a = 2, b = 2, c = 1 nên a - b + c = 1