The area (in sq. units) of the region bounded by the lines y = x + 4, y = x − 1, x = 1 and x = 4 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15
The lines y = x + 4 and y = x − 1 are parallel, and y = x + 4 is always 5 units above y = x − 1. So the height of the region is the same at every x:
\((x+4)-(x-1) = 5\)
\( \displaystyle A = \int_{1}^{4}5\,dx \)
\(= 5\times3 = 15\)
The region is a parallelogram with vertical sides of length 5 that are 3 units apart.