Có bao nhiêu số

D

- Hướng dẫn giải

Đáp án D.

Ta có ${\int }_0^a{\sin }^{5}x.\sin 2xdx={\int }_0^a{\sin }^{5}x.2\sin x\cos xdx=2{\int }_0^a{\sin }^{6}xd\left(\sin x\right)=2.{\overline{)\frac{{\sin }^{7}x}{7}}}_0^a=\frac{2}{7}{\sin }^{7}a=\frac{2}{7}$$\iff \sin x=1\iff x=\frac{\mathrm{\pi }}{2}+k2\mathrm{\pi } \left(\mathrm{k}\in \mathrm{\mathbb{Z}}\right).$ 

Ép cho $0<\frac{\mathrm{\pi }}{2}+k2\mathrm{\pi }<20\mathrm{\pi }\iff -\frac{1}{4}<\mathrm{k}<\frac{39}{4}\Rightarrow \mathrm{k}\in \left\{0;1;2;...;9\right\}.$