Question 46
Mathematics
Definite Integrals
Hard
The area enclosed between the curves y<sup>2</sup> = x and y = |x| is:
(A) <span class="math-tex">\(\dfrac23\)</span> sq. units.
(B) 1 sq. units.
(C) <span class="math-tex">\(\dfrac16\)</span> sq. units.
(D) <span class="math-tex">\(\dfrac13\)</span> sq. units.
View Dynamic Solution & Explanation ▼
Correct Solution: Option C
Step-by-step Solution:
The graphs will intersect at the points (1, 1) and (0, 0): \[ \text{Shaded area} = \int_0^1 \left( \sqrt{x} - x \right) \, dx = \left[ \frac{x^{2/3}}{2/3} - \frac{x^2}{2} \right]_0^1 \] \[ = \frac{2}{3} - \frac{1}{2} = \frac{1}{6} \]
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