Find the total area enclosed by y=x^3-4x and the x-axis, between the vertical lines x=-2 and x=3 draw a diagram to illustrate your solution.

Answer 1

Note: My video recording feature for some reason crashed when I went to do the 3rd integral. However it is the same steps as before. Hopefully the audio is still manageable to understand. I do make this note in the video but the positive 4 for the second integral is correct (reasoning in the video). The final answer should be 57/4

Answer 2

y = x³ - 4x = 0; x = 0 or x = ±2;

Area s = ∫_-2⁰(x³ - 4x)dx + ∫₀²(4x - x³)dx + ∫₂³(x³ - 4x)dx = (x⁴/4 - 2x²)_-2⁰ + (2x² - x⁴/4)₀² + (x⁴/4 - 2x²)₂³ =

-(4 - 8) + ((8 - 4) + (81/4 - 18) - (4 - 8) = 57/4 = 14.25