Question
Download Solution PDFमाना \(f(x) = \left\lbrace \begin{matrix} -2, & -2 \le x \le 0 \\\ x - 2, & 0 < x \le 2 \end{matrix} \right.\) और h(x) = f(|x|) + |f(x)| है।
तब \(\int_{-2}^2 h(x) dx\) किसके बराबर है?
- 2
- 4
- 1
- 6
Answer (Detailed Solution Below)
Option 1 : 2
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Detailed Solution
Download Solution PDFस्पष्टीकरण:
\(f(x) = \left\lbrace \begin{matrix} -2, & -2 \le x \le 0 \\\ x - 2, & 0 < x \le 2 \end{matrix} \right.\)
h(x) = f(|x|) + |f(x)|.
\(h(x) = \left\lbrace \begin{matrix} x - 2 + 2 - x , & 0 \le x \le 2 \\\ -x - 2 + 2& -2 \le x < 0 \end{matrix} \right.\)
अर्थात, \(h(x) = \left\lbrace \begin{matrix}0, & 0 \le x \le 2 \\-x & -2 \le x < 0 \end{matrix} \right.\)
इसलिए, \(\int_{-2}^2 h(x) dx\)
= \(\int_{-2}^0 h(x) dx\) + \(\int_0^2 h(x) dx\)
= \(\int_{-2}^0 (-x) dx\) + 0
= \([-{x^2\over2}]_{-2}^0\) = 2
विकल्प (1) सही है।
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