Find the area enclosed between the ellipse and the -axis.

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

Find the area enclosed between the ellipse

\displaystyle \frac{x^{2}}{9}+\frac{y^{2}}{4}=1

and the

x

-axis. (i) Rewrite the equation of the ellipse to express

y

explicitly in terms of

x

for the upper half of the ellipse. (ii) Set up a definite integral that represents the required area. (iii) Evaluate the integral to obtain the exact value of the area.

Related theory

Antiderivatives
Area Applications
Applications of Integration
Area under a curve
Area under simple curves

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