Question

the region bounded by the parabola x^2=y and the line y=x in the first quadrant is rotated about the y-axis to generate a solid. find the volume of the solid

Answer 1

Answer:

Parabola x^^2=y and the line

Step-by-step explanation:

first quadrant is rotated about the y-axis

Answer 2

Answer:

here is your answer mate

Step-by-step explanation:

If the axis of revolution is horizontal, then: {eq}V=2\pi\int_a^bp(y)f(y)dy {/eq} where {eq}p(y) {/eq} is the distance between the axis of revolution and the {eq}x {/eq}-axis. If the curve rotates around the {eq}x {/eq}-axis: {eq}V=2\pi\int_a^byf(y)dy {/eq}.

b) If the axis of revolution is vertical, then:{eq}\displaystyle V=2\pi\int_a^bp(x)f(x)dx {/eq} where {eq}p(x) {/eq} is the distance between the axis of revolution and the {eq}y {/eq}-axis. If the curve rotates around the {eq}y {/eq}-axis: {eq}\displaystyle V=2\pi\int_a^bxf(x)dx {/eq}.

hope it helps ☺️