Question

Find the exact area of the surface obtained by rotating the curve about the x-axis. y=sqrt(1+3x) 0 12 years ago

Answer 1

Use the formula \[A = \int\limits\limits(2πy) ds = \int\limits\limits(2π\sqrt{1+3x}\sqrt{1 + \left( \frac{ dy }{ dx } \right)^2} dx\]

Answer 2

dy/dx = 3/sqrt(1+3x)
\[A = \int\limits2π\sqrt{1+3x} \sqrt{1 + \frac{9}{1+3x}}dx\]
Solve for the integral and plug your upper limit as 4 and lower limit as 0

Answer 3

\[A = 2π \int\limits_{0}^{4} \sqrt{10+3x} dx\]
\[A = 2π \left[ \frac{ 2 }{ 9 } (1 + 3x)^{3/2} \right]_{0}^{4} = \frac{4π}{9} (13^{3/2}) - \frac{4π}{9}\]

Answer 4

ok thankyou so much