Volume of revolutions: Find the volume generated when the region bounded by y=x^3 and the x-axis between x=2 and x=7 is rotated through 360° about the x-axis.
Volume of revolutions: Find the volume generated when the region bounded by y=x^3 and the x-axis between x=2 and x=7 is rotated through 360° about the x-axis.
I know how to do it now. Thank you, I really appreciate your help!
This is not a correction - all you did was change the limits while keeping the working out with domain x∈[0,2] so this post is technically still incorrect.
Your last line is wrong (you are still using the limits 2 and 0)!
Is this right? ∫ πy² dx from x = 2 to x = 7 = ∫ π(x³)² dx from x = 2 to x = 7 = ∫ πx⁶ dx from x = 2 to x = 7 = 1/7 πx⁷ = 1/7π( 7⁷ - 2⁷) = 823415π/7 ≈ 369548 cubic metres
Is this right? ∫ πy² dx from x = 2 to x = 7 = ∫ π(x³)² dx from x = 2 to x = 7 = ∫ πx⁶ dx from x = 2 to x = 7 = 1/7 πx⁷ = 1/7π( 7⁷ - 2⁷) = 823415π/7 ≈ 369548 cubic metres
That's correct. One small thing: the units should only be cubic metres if the question refers to metres.