Tính pi/4 landa 0 ( 2x - sin x + 4 ) dx

11/22

Tính \[\int\limits_0^{\frac{\pi }{4}} {\left( {2x - \sin x + 4} \right){\rm{d}}x} \]

\[\frac{{{\pi ^2} + 16\pi + 8\sqrt 2 - 16}}{{16}}\] .

\[\frac{{{\pi ^2} + 16\pi + 2\sqrt 2 - 4}}{{16}}\].

\[\frac{{{\pi ^2} + 16\pi + 8\sqrt 2 }}{{16}}\].

\[\frac{{{\pi ^2} + 16\pi - 16}}{{16}}.\]

Giải thích

\[\int\limits_0^{\frac{\pi }{4}} {\left( {2x - \sin x + 4} \right){\rm{d}}x} \]\[ = \left( {{x^2} + \cos x + 4x} \right)\left| \begin{array}{l}\frac{\pi }{4}\\0\end{array} \right. = \frac{{{\pi ^2}}}{{16}} + \frac{{\sqrt 2 }}{2} + \pi - 1 = \frac{{{\pi ^2} + 16\pi + 8\sqrt 2 - 16}}{{16}}.\]