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Manipal MET2023MathematicsArea Under Curves

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

Options

  1. A15 sq units
  2. B17 2 sq units
  3. C13 sq units
  4. D16 sq units

Correct answer

B. 17 2 sq units

Step-by-step solution

Required area = | ₁^6 | 5-x|d x|= | ₁^5-(5-x) d x+ ₅^6(5-x) d x |= | [-5 x+ x^2 2 ]₁^5+ [5 x- x^2 2 ]₅^6 |= | [-25+ 25 2 +5- 1 2 ]+ [30-18-25+ 25 2 ] |= [ -50+25+10-1 2 ]+ [ -26+25 2 ]= |-8- 1 2 |= 17 2 sq units

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