Integral Calculus
Area
MMTS_Full_Test_01
Grade 12

Question:

The smaller area (in sq. units) included between the curves $\sqrt{x}+\sqrt{|y|}=1$ and $|x|+|y|=1$ is
$\dfrac{1}{3}$
$\dfrac{4}{3}$
$\dfrac{2}{3}$
$\dfrac{5}{3}$

Step-by-Step Solution

Key Concept: Plot both curves; find area between them in first quadrant and multiply
In first quadrant: area between $\sqrt{x}+\sqrt{y}=1$ and $x+y=1$: $\int_0^1[(1-\sqrt{x})^2-(1-x)]dx=1/3-1/2+...$. Total smaller area $=2/3$.
Correct Answer: 3

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