Q24 / 50 · Manipal (MET) 2023 · Mathematics

The area bf the region bounded by the curves $y=|5-x|, x=1, x=6$ and the $X$-axis

  • A
    15 sq units
  • Correct answer
    B
    $\frac{17}{2}$ sq units
  • C
    13 sq units
  • D
    16 sq units

Solution

Required area $=\left|\int_1^6\right| 5-x|d x|$ $=\left|\int_1^5-(5-x) d x+\int_5^6(5-x) d x\right|$ $=\left|\left[-5 x+\frac{x^2}{2}\right]_1^5+\left[5 x-\frac{x^2}{2}\right]_5^6\right|$ $=\left|\left[-25+\frac{25}{2}+5-\frac{1}{2}\right]+\left[30-18-25+\frac{25}{2}\right]\right|$ $=\left[\frac{-50+25+10-1}{2}\right]+\left[\frac{-26+25}{2}\right]$ $=\left|-8-\frac{1}{2}\right|=\frac{17}{2}$ sq units

Hence, the correct answer is option: 'B'.

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