Question

Find the volume of the solid that results when the region above x-axis and below the ellipse x²/a²+y²/b²=1 (a>0,b>0)
is revolved about axis.​

Answer 1

Step-by-step explanation:

When ellipse is rotated about major axis:

Take a small disc at a length of x from the centre of thickness dx. Then the volume of solid obtained by rotation will be ∫−aa(Area)dx

Area of disc =πr2

r can be calculated from the equation of ellipse as

a2x2+b2r2=1

⇒r2=b2(1−a2x2)=a2b2(a2−x2)

∴Volumemajor axis=∫−aaπa2b2(a2−x2)dx=[πb2x−3a2πb2x3]−aa=34πab2

Case (ii): When ellipse is rotated about minor axis:

Following similar procedure as case (i),

r

Answer 2

Answer:

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