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AP EAMCET · Maths · Area Under Curves

The area of the region (in sq. units) enclosed between the curves \(y=|x|, y=[x]\) and the ordinates \(x=-1, x=0, x=1\) is

  1. A 2
  2. B \(\frac{3}{2}\)
  3. C 3
  4. D \(\frac{5}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) 2

Step-by-step Solution

Detailed explanation

\(A = \int_{-1}^{0} (-x - (-1)) dx + \int_{0}^{1} (x - 0) dx\) \(A = \left[ -\frac{x^2}{2} + x \right]_{-1}^{0} + \left[ \frac{x^2}{2} \right]_{0}^{1}\) \(A = \left(-\frac{0^2}{2} + 0\right) - \left(-\frac{(-1)^2}{2} + (-1)\right) + \left(\frac{1^2}{2} - \frac{0^2}{2}\right)\)…