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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2008 · Mathematics · Area Under Curves

The area of the plane region bounded by the curves x+2 y^2=0 and...

The area of the plane region bounded by the curves x+2y2=0x+2 y^2=0 and x+3y2=1x+3 y^2=1 is equal toThe area of the plane region bounded by the curves x+2 y^2=0 and x+3 y^2=1 is equal toThe area of the plane region bounded by the curves x+2 y^2=0 and x+3 y^2=1 is equal to

Options

  1. A53\frac{5}{3}
  2. B13\frac{1}{3}
  3. C23\frac{2}{3}
  4. D43\frac{4}{3}

Correct answer

D. 43\frac{4}{3}

Step-by-step solution

Solving the equations we get the points of intersection (−2,1)(-2,1) and (−2,−1)(-2,-1) The bounded region is shown as shaded region. The required area =2∫01(1−3y2)−(−2y2)=2∫01(1−y2)dy=2[y−y33]01=2×23=43.\begin{aligned}& \text{ The required area }=2 \int_0^1\left(1-3 y²\right)-\left(-2 y²\right) \\ & =2 \int_0^1\left(1-y²\right) d y=2\left[y-\frac{y^3}{3}\right]_0^1=2 \times \frac{2}{3}=\frac{4}{3} . \end{aligned}The area of the plane region bounded by the curves x+2 y^2=0 and x+3 y^2=1 is equal to
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