The area enclosed between the curves y 2 = x and y = |x| is:

The graphs will intersect at the points (1, 1) and (0, 0): \[ Shaded area = ∈t 0 1 ( √(x) - x ) \, dx = [ x 2/3 2/3 - x 2/2 ] 0 1 \] \[ = 2/3 - 1/2 = 1/6 \]

The area enclosed between the curves... - Solved

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Question 46

Mathematics Definite Integrals Hard

The area enclosed between the curves y2 = x and y = |x| is:

(A) \(\dfrac23\) sq. units.

(B) 1 sq. units.

(C) \(\dfrac16\) sq. units.

(D) \(\dfrac13\) sq. units.

✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The graphs will intersect at the points (1, 1) and (0, 0): \[ \text{Shaded area} = \int_0^1 \left( \sqrt{x} - x \right) \, dx = \left[ \frac{x^{2/3}}{2/3} - \frac{x^2}{2} \right]_0^1 \] \[ = \frac{2}{3} - \frac{1}{2} = \frac{1}{6} \]