Final answer:
To find the area inside the curves 3sin(theta) and 3cos(theta), set the curves equal to each other, solve for theta, and calculate the difference in areas using integration. The correct answer is B) 6π.
Step-by-step explanation:
To find the area inside the curves 3sinθ and 3cosθ, we can set them equal to each other and solve for θ. This will give us the boundaries of the region.
Setting 3sinθ = 3cosθ, we can divide both sides by 3 to get sinθ = cosθ. From this equation, we can see that the values of θ that satisfy this condition are θ = 45° and θ = 225°.
The area inside the curves is the difference in the areas between the two curves. We can calculate this by integrating the curves from 45° to 225°:
A = ∫(3sinθ)dθ - ∫(3cosθ)dθ = -6∫cosθdθ = -6sinθ|_45^225= 0 - (-6) = 6.
Therefore, the correct answer is B) 6π.