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AP EAMCET · Maths · Area Under Curves

The area (in square units) bounded by the curves \(y=2 x^2\) and \(y=\max \{x-[x], x+|x|\}\) in between the lines \(x=0\) and \(x=2\) is

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

Answer & Solution

Correct Answer

(D) 2

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & y=\max \cdot\{x-[x], \quad x+|x|\} \\ & \Rightarrow \quad y= \begin{cases}2 x, & x \geq 0 \\ \{x\}, & x \begin{aligned} & =\left|\int_0^1 2 x d x-\int_0^1 2 x^2 d x\right|+\left|\int_1^2 2 x^2 d x-\int_1^2 2 x d x\right| \\ & =\left|\left[\frac{2…