Bài tập 3.52 trang 182 SBT Toán 12

Tìm khẳng định đúng trong các khẳng định sau:

A. \(\int \limits_0^\pi  \left| {\sin \left( {x + \frac{\pi }{4}} \right)} \right|dx = \int \limits_0^\pi  \left| {\sin \left( {x - \frac{\pi }{4}} \right)} \right|dx\)

B. \(\int \limits_0^\pi  \left| {\sin \left( {x + \frac{\pi }{4}} \right)} \right|dx = \int \limits_0^\pi  \left| {\cos \left( {x + \frac{\pi }{4}} \right)} \right|dx\)

C. \(\begin{array}{l}
\int \limits_0^\pi  \left| {\sin \left( {x + \frac{\pi }{4}} \right)} \right|dx\\
 = \int \limits_0^{\frac{{3\pi }}{4}} \sin \left( {x + \frac{\pi }{4}} \right)dx - \int \limits_{\frac{{3\pi }}{4}}^\pi  \sin \left( {x + \frac{\pi }{4}} \right)dx
\end{array}\)

D. \(\int \limits_0^\pi  \left| {\sin \left( {x + \frac{\pi }{4}} \right)} \right|dx = 2\int \limits_0^{\frac{\pi }{4}} \sin \left( {x + \frac{\pi }{4}} \right)dx\)