Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Find the volume of the frustrum of the right circular cone generated by rotating the line y = 3x+1 about the x-axis between x = 0 and x = 2.

Sagot :

Answer:

38π cubic units

Step-by-step explanation:

The volume V = ∫₀²πy²dx  

Since y = 3x + 1, dy = 3dx ⇒ dx = dy/3

So, when x = 0, y = 3(0) + 1 = 0 + 1 = 1

when x = 2, y = 3(2) + 1 = 6 + 1 = 7

So, changing the variable to y and the limits of integration from y = 1 to y = 7, we have

V = ∫₀²πy²dx

V = π∫₁⁷y²dy/3

V = π[y³/3]₁⁷/3

V = π[y³]₁⁷/9

V = [7³ - 1³]π/9

V = [343 - 1]π/9

V = 342π/9

V = 38π cubic units