The option(s) with the values of a and L that satisfy the following equation is(are)
$$\frac{\int_{0}^{4\pi}e^t (\sin^6 at + \cos^4 at)dt}{\int_{0}^{\pi}e^t (\sin^6 at + \cos^4 at)dt} = L$$ ?

A

$$a = 2, L = \frac{e^{4\pi} - 1}{e^{\pi} - 1}$$

B

$$a = 2, L = \frac{e^{4\pi} + 1}{e^{\pi} + 1}$$

C

$$a = 4, L = \frac{e^{4\pi} - 1}{e^{\pi} - 1}$$

D

$$a = 4, L = \frac{e^{4\pi} + 1}{e^{\pi} + 1}$$