JEE MAIN - Mathematics (2021 - 22th July Evening Shift - No. 20)
The area (in sq. units) of the region bounded by the curves x2 + 2y $$-$$ 1 = 0, y2 + 4x $$-$$ 4 = 0 and y2 $$-$$ 4x $$-$$ 4 = 0, in the upper half plane is _______________.
Answer
2
Explanation
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Required area (shaded)
$$ = 2\left[ {\int\limits_0^2 {\left( {{{4 - {y^2}} \over 4}} \right)dy - \int\limits_0^1 {\left( {{{1 - {x^2}} \over 2}} \right)dx} } } \right]$$
$$ = 2\left[ {{4 \over 3} - {1 \over 3}} \right] = (2)$$
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