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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Area Under Curves

NDA 2026 · Mathematics · Area Under Curves

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is...

Passage: Consider the curves y=x2y=x^2 and y=2∣x∣y=2|x|.

Question: What is the area bounded by the curves, the lines x=0x=0 and x=1x=1 ?

Options

  1. A11 square unit
  2. B23\dfrac{2}{3} square unit
  3. C12\dfrac{1}{2} square unit
  4. D13\dfrac{1}{3} square unit

Correct answer

B. 23\dfrac{2}{3} square unit

Step-by-step solution

For x∈[0,1]x \in [0,1], the curve y=2∣x∣y = 2|x| becomes y=2xy = 2x.

In the interval x∈[0,1]x \in [0,1], 2x≥x22x \ge x^2.

The required area is given by the integral:

A=∫01(2x−x2)dxA = \int_{0}^{1} (2x - x^2) dx

A=[x2−x33]01A = \left[ x^2 - \dfrac{x^3}{3} \right]_{0}^{1}

A=1−13=23A = 1 - \dfrac{1}{3} = \dfrac{2}{3} square units.
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