Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

The equation of the sides of the triangle are y = 2x + 1, y = 3x + 1 and x = 4.

So, solving above equations, we get the vertices of triangle are A (0, 1), B (4, 13) and c (4, 9).

We can see that Area (ΔACB) = Area (OLBAO) - Area (OLCAO)

= (24 + 4) – (16 + 4)

= 28 – 20

= 8 units.

Therefore, the required are is 8 units.

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