Question

Hi, I need help with the steps!

Use a definite integral to find an expression that represents the area of the region between the given curve and the x-axis on the interval [0,b].

y=6pi x^2

Answer 1

@oldrin.bataku

Answer 2

x is restricted to 0 and b, then we sub this domain to find region of y. y then must be between 0 and 6pib^2.

Answer 3

area is just
\[\int\limits\limits_{0}^{b} \int\limits_{0}^{6\pi b^2} 1 dydx\]

Answer 4

\[\int\limits_{0}^{b}y dx =\int\limits_{0}^{b}6\pi x^2 dx=6\pi \int\limits_{0}^{b} x^2 dx\]
\[=6\pi [\frac{x^3}{3}]_{0}^{b} =\frac {6\pi}{3}[{x^3}]_{0}^{b}= 2\pi [b^3-0^3] = 2\pi b^3\]

Answer 5

soz, the upper bound of y region should be 6 pix^2.

Answer 6

SO the final answer is 2pi b^3 @dpasingh