The interior surface of the bowl of a goblet is formed by rotating y=3x2, 0x2 around the y-axis. Wine is poured into the goblet so that it fills 45% of its capacity. Measured from the bottom of the bowl, what is the depth of the wine?
I know the a,b values are 0,2. This is how I set the integral up.
2pi x Integral((x)(3x^2))
2pi x integral 3x^4
Can someone help me solve this problem please?