The option(s) with the values of and that satisfy the equation _0^ 4 e^t ( ^6 at + ^4…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The option(s) with the values of

a

and

L

that satisfy the equation

\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

is/are: (1)

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

(2)

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

(3)

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

(4)

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