Integral Application

Question

Find the area of the region bounded by the curve y²= x and the lines x=1, x=4 and the x-axis.

Answer 1

Required area = Area of ABCD \(= \int ^4 _1\) ydx

\(=\int ^4 _1 \sqrt {x}dx\)

\(=\frac {2}{3} [(4)^{3/2} - (1) ^{3/2} ]\)

\(=\frac {2}{3} (8-1) = \frac {14}{3}\)units