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BITSAT 2019
Exam
BITSAT
Year
2019
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2019 · Mathematics · Area Under Curves

Area bounded by two branches of the curve (y - x)2 = x^ 3 and x = 1...

Area bounded by two branches of the curve (y−x)2=x3\left(y - x\right)2 = x^{3} and x = 1 isArea bounded by two branches of the curve (y - x)2 = x^ 3 and x = 1 is

Options

  1. A54squnit\dfrac{5}{4}squnit
  2. B32squnit\dfrac{3}{2}squnit
  3. C14squnit\dfrac{1}{4}squnit
  4. D45squnit\dfrac{4}{5}squnit

Correct answer

D. 45squnit\dfrac{4}{5}squnit

Step-by-step solution

Given, curve is (y−x)2=x3\left(y - x\right)2 = x^{3}

⇒y−x=±xx⇒ y - x = \pm x\sqrt{x}

⇒y=x±xx⇒ y = x \pm x\sqrt{x}

Area bounded by two branches of the curve (y - x)2 = x^ 3 and x = 1 is

∴∴ Area bounded =∣∫01{(x+xx)−(x−xx)}dx∣= \left|{∫}_{0}^{1}\left\{\left(x + x\sqrt{x}\right) - \left(x - x\sqrt{x}\right)\right\}dx\right|

=∣2∫01x3/2dx∣=45squnit= \left|2{∫}_{0}^{1}x^{3 / 2}dx\right| = \dfrac{4}{5}squnit

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