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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Area Under Curves

The area (in sq. units) of the region enclosed by the curves y = x...

The area (in sq. units) of the region enclosed by the curves y=x2−1y = {x}^{2} - 1 and y=1−x2y = 1 - {x}^{2} is equal to:The area (in sq. units) of the region enclosed by the curves y = x ^ 2 - 1 and y = 1 - x ^ 2 is equal to:

Options

  1. A43\dfrac{4}{3}
  2. B83\dfrac{8}{3}
  3. C72\dfrac{7}{2}
  4. D163\dfrac{16}{3}

Correct answer

B. 83\dfrac{8}{3}

Step-by-step solution

The area (in sq. units) of the region enclosed by the curves y = x ^ 2 - 1 and y = 1 - x ^ 2 is equal to:

Given curves are

y=x2−1y = {x}^{2} - 1

and

y=1−x2y = 1 - {x}^{2}

so intersection point are \left(\pm 1, 0\right)</p><p></p><p>∴boundedarea</p><p>bounded area</p><p>= 4{∫}_{0}^{1}\left(1 - {x}^{2}\right)dx</p><p></p><p>= 4{\left[x - \dfrac{{x}^{3}}{3}\right]}_{0}^{1}</p><p></p><p>= 4\left(1 - \dfrac{1}{3}\right)\dfrac{8}{3}sq \cdot units

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