JEE MAIN - Mathematics (2020 - 6th September Evening Slot - No. 3)
The area (in sq. units) of the region enclosed
by the curves y = x2 – 1 and y = 1 – x2 is equal to :
by the curves y = x2 – 1 and y = 1 – x2 is equal to :
$${8 \over 3}$$
$${4 \over 3}$$
$${7 \over 2}$$
$${{16} \over 3}$$
Explanation
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A = $$\int\limits_{ - 1}^1 {\left( {\left( {1 - {x^2}} \right) - \left( {{x^2} - 1} \right)} \right)dx} $$
= $$\int\limits_{ - 1}^1 {\left( {2 - 2{x^2}} \right)dx} $$
= $$4\int\limits_0^1 {\left( {1 - {x^2}} \right)dx} $$
= $$4\left( {x - {{{x^3}} \over 3}} \right)_0^1$$
= $$4\left( {{2 \over 3}} \right)$$ = $${8 \over 3}$$
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