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find the area of the region bounded by the curve y...

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:

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

\begin{align}Area \;of\; ABCD = \int_{1}^{4} y.dx \end{align}

\begin{align} = \int_{1}^{4} \sqrt{x}.dx \end{align}

\begin{align} =\left[\frac{x^\frac{3}{2}}{\frac{3}{2}}\right]_1^4 \end{align}

\begin{align} =\frac{2}{3}\left[(4)^\frac{3}{2} - (1)^{\frac{3}{2}}\right] \end{align}

\begin{align} =\frac{2}{3}\left[8 -1\right] \end{align}

\begin{align} =\frac{14}{3}\; Units \end{align}

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

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

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