Find the volume of the solid obtained by rotating the region enclosed by the graphs

Question

If x≥0, find the volume of the solid obtained by rotating the region enclosed by the graphs about the line 𝑦=−8.

Equation for the curves: 𝑦=2−𝑥, 𝑦=𝑥2, 𝑥=0

Answer 1

2 - x = x²; x = 1 or x = - 2. So, 0 ≤ x ≤ 1

By washer method volume v = π∫₀¹[(10 - x)² - (x² + 8)²]dx = π∫₀¹(36 - 20x - 15x²)dx = π(36x - 10x² - 5x³)₀¹ =

21π

Answer 2

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