Final answer:
To find the area of the region bounded by the curves y=5x^3 and y=45x, you need to determine the points of intersection between the two curves and integrate each curve separately.
Step-by-step explanation:
To find the area of the region bounded by the curves y=5x^3 and y=45x, we need to determine the points of intersection between the two curves. Setting the two equations equal to each other, we have 5x^3 = 45x. Dividing both sides by x, we get 5x^2 = 45. Solving for x, we find that x = ±3.
We can then integrate each curve separately to find the areas under the curves between the x-values of -3 and 3. The area under the curve y=5x^3 is given by the definite integral ∫(from -3 to 3) 5x^3 dx. The area under the curve y=45x is given by the definite integral ∫(from -3 to 3) 45x dx. Evaluating these integrals will give us the areas of the regions bounded by the curves.