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BITSAT 2024Paper 2
Exam
BITSAT
Year
2024
Paper
Paper 2
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2024 · Paper 2 · Mathematics · Area Under Curves

The area of the region bounded by the curves x=y^2-2 and x=y is

The area of the region bounded by the curves x=y2−2x=y^2-2 and x=yx=y isThe area of the region bounded by the curves x=y^2-2 and x=y is

Options

  1. A94\frac{9}{4}
  2. B99
  3. C92\frac{9}{2}
  4. D97\frac{9}{7}

Correct answer

C. 92\frac{9}{2}

Step-by-step solution

Given, x=y2−2andx=yx=y^2-2 and x=y. The area of the region bounded by the curves x=y^2-2 and x=y is On solving, x=y2−2andx=yx=y^2-2 and x=y, we get (−1,−1)and(2,2)(-1,-1) and (2,2). Area of the shaded region, A=∫−12ydy−∫−12(y2−2)dy=[y22−y33+2y]−12=(42−83+4)−(12+13−2)=103+76=276=92.\begin{aligned} & A=\int_{-1}^2 y d y-\int_{-1}^2\left(y^2-2\right) d y \\ & =\left[\frac{y^2}{2}-\frac{y^3}{3}+2 y\right]_{-1}^2=\left(\frac{4}{2}-\frac{8}{3}+4\right)-\left(\frac{1}{2}+\frac{1}{3}-2\right) \\ & =\frac{10}{3}+\frac{7}{6}=\frac{27}{6}=\frac{9}{2}. \end{aligned}
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