Find the area bounded by the ellipse a2x2+b2y2=1and the ordinates x=0andx=ae, where, b2=a2(1−e2)ande<1.

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Find the area bounded by the ellipse {{{x}^{{2}}}}{{{a}^{{2}}}

Question

Find the area bounded by the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ and the ordinates $x = 0$ and $x = a e$ , where, $b^{2} = a^{2} (1 - e^{2})$ and $e < 1$ .

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Find the area bounded by the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

and the ordinates

x = 0

and

x = a e

, where,

b^{2} = a^{2} (1 - e^{2})

and

e < 1

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Question Text

Find the area bounded by the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

and the ordinates

x = 0

and

x = a e

, where,

b^{2} = a^{2} (1 - e^{2})

and

e < 1