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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Let R be the region bounded by the x-axis, the graph of y= √(x + 1), and the line x = 3. Find the area of the region R
Solution:
The region bounded by the curve y= √(x+1) and the line x = 3 is shown in the diagram below. The shaded area lies above the x axis because the function y= √(x + 1) lies above the x - axis. Therefore the region R bounded by the curve and the line x = 3 is given by:
The Area ABC = \(\int_{-1}^{3}\sqrt{x+1}dx\)
= \([\frac{(x+1)^{\frac{1}{2}+1}}{\frac{3}{2}}]_{-1}^{3}\)
= \(\frac{2}{3}[(x+1)^{\frac{3}{2}}]_{-1}^{3}\)
= \(\frac{2}{3}[(3+1)^{\frac{3}{2}} - (-1 + 1)^{\frac{3}{2}}]\)
= \(\frac{2}{3}[(4)^{\frac{3}{2}} - (0)^{\frac{3}{2}}]\)
= \(\frac{2}{3}[\sqrt{64}]\)
= \(\frac{2}{3}[8]\)
= 16/3 units2
Let R be the region bounded by the x-axis, the graph of y= √(x+1), and the line x = 3. Find the area of the region R
Summary:
The area of the region R is 16/3 units2.
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