The area of the region bounded by the curve y = x + 1, x-axis and the lines x = 2 and x = 3 is ______________.

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Solution

To find: area of the region bounded by the curve y = x + 1, x-axis and the lines x = 2 and x = 3

The required area of the region = $\int_{2}^{3} y d x$
Thus,
$Required area = \int_{2}^{3} y d x = \int_{2}^{3} (x + 1) d x = {(\frac{x^{2}}{2} + x)}_{2}^{3} = (\frac{3^{2}}{2} + 3) - (\frac{2^{2}}{2} + 2) = (\frac{9}{2} + 3) - (2 + 2) = (\frac{9 + 6}{2} - 4) = \frac{15}{2} - 4 = \frac{15 - 8}{2} = \frac{7}{2} Thus, Area = \frac{7}{2} sq . units$

Hence, the area of the region bounded by the curve y = x + 1, x-axis and the lines x = 2 and x = 3 is $\frac{7}{2} sq . units .$

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