Volumes (1 Viewer)

[sonnylongbottom]

Find the volume generated when the region bounded by the given curve and lines is rotated about the x-axis

y=x^2+2 and y=x+4

yea havin troubles with volumes.

 

[Trebla]

This is just a typical volume between two curves:
V = π(from -1 to 2)∫(x + 4)² dx - π(from -1 to 2)∫(x² + 2)² dx
= π(from -1 to 2)∫(x² + 8x + 16 - [x⁴ + 4x² + 4]) dx
= π(from -1 to 2)∫(x² + 8x + 16 - x⁴ - 4x² - 4]) dx
= π(from -1 to 2)∫(- 3x² + 8x + 12 - x⁴) dx
= π [- x³ + 4x² + 12x - x⁵/5] (from -1 to 2)
= π (128/5 - (- 34/5))
= 162π/5 cubic units

check my working...