Jawab: C

$$\begin{array}{rl}{\int }_{-2}^0(\cos (-\pi kx)+\frac{6x^2-10x+7}{k+2})dx& =(k-2)(k+7)\\ \\ {\int }_{-2}^0(\cos (-\pi kx))dx+{\int }_{-2}^0\left(\frac{6x^2-10x+7}{k+2}\right)dx& =(k-2)(k+7)\\ \\ {\int }_{-2}^0(\cos (-\pi kx))\frac{d(\cos (-\pi kx))}{-\pi k}+\frac{1}{k+2}{\int }_{-2}^0(6x^2-10x+7)dx& =(k-2)(k+7)\\ \\ \frac{1}{-\pi k}{\int }_{-2}^0(\cos (-\pi kx))d(\cos (-\pi kx))+\frac{1}{k+2}{\int }_{-2}^0(6x^2-10x+7)dx& =(k-2)(k+7)\\ \\ \frac{1}{-\pi k}{[\sin (-\pi kx)]}_{-2}^0+\frac{1}{k+2}{[2x^3-5x^2+7x]}_{-2}^0& =(k-2)(k+7)\\ \\ \frac{1}{-\pi k}[\sin (-\pi k.0)-\sin (-\pi k.-2)]+\frac{1}{k+2}([2.(0{)}^3-5.(0{)}^2+7.(0)]-[2.(-2{)}^3-5.(-2{)}^2+7.(-2)])& =(k-2)(k+7)\\ \\ \frac{1}{-\pi k}[\sin 0-\sin 2\pi ]+\frac{1}{k+2}(\left[0\right]-[-16-20-14])& =(k-2)(k+7)\\ \\ \frac{1}{-\pi k}[0-0]+\frac{1}{k+2}(\left[0\right]-[-50])& =(k-2)(k+7)\\ \\ \frac{50}{k+2}& =(k-2)(k+7)\\ \\ 50& =(k-2)(k+2)(k+7)\end{array}$$

Menyelesaikan bentuk $(k-2)(k+2)(k+7)=50$

Faktor dari 50 adalah 1, 2, 5, 10, 25, 50

Tes nilai k yang sesuai agar menghasilkan faktor-faktor di atas.

Untuk $k=3$

$$\begin{array}{rl}(k-2)(k+2)(k+7)& =50\\ \\ (3-2)(3+2)(3+7)& =50\\ \\ 1.5.10& =50\\ \\ 50& =50\end{array}$$

Nilai k yang sesuai adalah 3

Maka $k+5=8$