The area of the region bounded by the line $2 y+x=8, x-$ axis and the lines $x=2$ and $x=4$ is

The area of the region bounded by the line $2 y+x=8, x-$ axis and the lines $x=2$ and $x=4$ is
  1. 6 sq. units
  2. 5 sq. units
  3. 4 sq. units
  4. 10 sq. units

Solution

The required area $=\int_2^4 \frac{8-\mathrm{x}}{2} \mathrm{dx}$ $=\left[4 x-\frac{x^2}{4}\right]_2^4=(16-4)-(8-1)=5 \text { sq unit }$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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