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Question: The area enclosed by the parabola ay = 3(a<sup>2</sup> – x<sup>2</sup>) and the x - axis is...

The area enclosed by the parabola ay = 3(a2 – x2) and the x - axis is

A

4a2 sq. units

B

a2 sq. units

C

6a2 sq. units

D

5a2 sq. units

Answer

4a2 sq. units

Explanation

Solution

The parabola cuts the x-axis at points (–a, 0) and (a, 0).

A = aaydx\int _ { - a } ^ { a } y d x = 2 3a0a(a2x2)dx\frac { 3 } { a } \int _ { 0 } ^ { a } \left( a ^ { 2 } - x ^ { 2 } \right) d x = 4a2 sq. units