Grade 12Algebra
how to calculate area of an eclipse using integration
how to calculate area of an eclipse using integration
1 Answer
Vikas TU
The area of elipse as we probably am aware is π .a .b where an and b are the semi-significant hub and semi-minor hub of the oval.
By utilizing integrals, we can discover the zone of oval, we will discover the zone of one quarter and increase it by 4.
Recipe for one fourth of oval is
y=b⋅((1−x2 )/a2 )
This quarter-oval has focus at (0,0). Its zone is
A=∫_0^a▒〖b⋅((1-x^2 )/a^2)〗
Consequently the aggregate range of the circle is
A=4∫_0^a▒〖b⋅((1-x^2 )/a^2)〗
Presently substitute sin t = x/a
=> dx = a cos t dt
Consequently the Area of circle is π .a .b
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