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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Area Under Curves

NDA 2013 · Mathematics · Area Under Curves

What is the area of the parabola x^2=y bounded by the line y=1 ?

What is the area of the parabola x2=yx^2=y bounded by the line y=1y=1 ?

Options

  1. A13\frac{1}{3} square unit
  2. B23\frac{2}{3} square unit
  3. C43\frac{4}{3} square units
  4. D2 square units

Correct answer

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

Step-by-step solution

RequiredareaisareaAOBRequired area is area AOB=∫01y⋅dy=[(y)3/23/2]01=23 square units \begin{aligned} & =\int_0^1 \sqrt{y} \cdot d y=\left[\frac{(y)^{3 / 2}}{3 / 2}\right]_0^1 \\ & =\frac{2}{3} \text{ square units } \end{aligned}$$
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