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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Mathematics
Chapter
Differential Equations

BITSAT 2010 · Mathematics · Differential Equations

The area of the region bounded by the curve y=x|x|, x -axis and the...

The area of the region bounded by the curve y=x∣x∣,xy=x|x|, x-axis and the ordinates x=1,x=−1x=1, x=-1 is given by :

Options

  1. Azero
  2. B(13\frac{1}{3})
  3. C(23\frac{2}{3})
  4. D1

Correct answer

C. (23\frac{2}{3})

Step-by-step solution

The area of the region bounded by the curve y=f(x)y=f(x) and the ordinates x=a,x=bx=a, x=b is given by (\text{Area }=\left|\int_a^b y d x\right|) According to the question, (y=x|x|= {x2,x≥0−x2,x<0\begin{cases}x^2, & x \geq 0 \\ -x², & x < 0\end{cases}) Required area == area of region (\mathrm{OAB}+) area of region (\mathrm{OCD}) (=2 \times) Area of region (\mathrm{OAB}) (=2 \int_0^1 x² d x=\frac{2}{3}s q). units
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