The first derivative of the function f is defined by f′(x) = sin(x3 − x) for 0 ≤ x ≤ 2. On what intervals is f increasing?.
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The volume of the base of the region enclosed by the parabola is; V = 9
<h3>Integral Volume of a Solid</h3>The length of each cross-section is determined by the horizontal distance (parallel to the x-axis) from one end of the parabola to the other.
Thus;
y = 3 - 2x²
Making x the subject gives us;
x = ±√[(3 - y)/2]
Thus;
The horizontal distance is;
√[(3 - y)/2] - (-√[(3 - y)/2])
⇒ 2√[(3 - y)/2]
The area of each cross-section is simply the square of the section's side length, so the area would be;
A = (2√[(3 - y)/2])²
A = 6 - 2y
Thus, volume is;
V =
Solving this gives V = 9
Read more about integral volume of solids at; brainly.com/question/14845570