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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Area Under Curves

NDA 2024 · Mathematics · Area Under Curves

Paragraph: The area bounded by the parabola y^2=k x and the line...

Paragraph: The area bounded by the parabola y2=kxy^2=k x and the line x=kx=k, where k>0k > 0, is 43\frac{4}{3} square units.
Question: What is the area of the parabola bounded by the latus rectum?

Options

  1. A16\frac{1}{6} square unit
  2. B23\frac{2}{3} square unit
  3. C1 square unit
  4. D43\frac{4}{3} square unit

Correct answer

A. 16\frac{1}{6} square unit

Step-by-step solution

So equation of parabola is y2=x(k=1)4a=1,a=14\mathrm{y}^2=\mathrm{x}(\mathrm{k}=1)4 a=1, a=\frac{1}{4} Area of parabola y2=x\mathrm{y}^2=\mathrm{x} and latus rectum at x=14\mathrm{x}=\frac{1}{4} is =2∫014xdx=2×23(14)32=43×18=16=2 \int_0^{\frac{1}{4}} \sqrt{\mathrm{x}} \mathrm{dx}=2 \times \frac{2}{3}\left(\frac{1}{4}\right)^{\frac{3}{2}}=\frac{4}{3} \times \frac{1}{8}=\frac{1}{6} sq. units
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