# Thread: area of surface by rotating the curve

1. ## area of surface by rotating the curve

Find the area of the surface generated by rotating the curve x=1 + t^2, y =t from t = 0 to t= 4 about the x-axis

can u show ur steps.... need to learn this for a test

thankx

2. Originally Posted by victorxz90044
Find the area of the surface generated by rotating the curve x=1 + t^2, y =t from t = 0 to t= 4 about the x-axis

can u show ur steps.... need to learn this for a test

thankx

$A = \int_{t_1}^{t_2} 2\pi \cdot r(t) \cdot \sqrt{[x'(t)]^2 + [y'(t)]^2} \, \, dt
$

3. ## detail

$r(t)$ = radius of revolution of the curve in terms of t
$\sqrt{[x'(t)]^2 + [y'(t)]}$ ... you should know what this represents.