If g(x) = ∫₀ˣ cos(4t)dt, then g(x + π) equals:

Given g(x) = ∫₀ˣ cos(4t)dt
We need to find g(x + π).
Let's first find the expression for g(x):
g(x) = ∫₀ˣ cos(4t)dt = [sin(4t)/4]₀ˣ = sin(4x)/4
Now, let's find g(x + π):
g(x + π) = sin(4(x + π))/4 = sin(4x + 4π)/4
Since sin(θ + 2nπ) = sin(θ) for any integer n, we have:
g(x + π) = sin(4x + 4π)/4 = sin(4x)/4
Therefore, g(x + π) = g(x)
Let's check the options:
Option A: g(x).g(π) = (sin(4x)/4)(sin(4π)/4) = 0
Option B: g(x) + g(π) = sin(4x)/4 + sin(4π)/4 = sin(4x)/4
Option C: g(x) - g(π) = sin(4x)/4 - sin(4π)/4 = sin(4x)/4
Option D: g(x)g(π) = (sin(4x)/4)(sin(4π)/4) = 0
Comparing the options with g(x + π) = sin(4x)/4 = g(x), we see that options B and C are correct. However, only one answer can be selected. Let's re-examine the problem.
Since g(x + π) = g(x), and g(π) = sin(4π)/4 = 0, the correct option would be g(x) + g(π) = g(x), or g(x) - g(π) = g(x). The question is ambiguous. The options should be corrected or a proper explanation provided to resolve this issue. The solution should be either g(x) or g(x) + g(π) = g(x) , but the options don't correctly reflect this.