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Draw a rough sketch of the curve y = √(x – 1) in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.
Draw a rough sketch of the curve y = √(x – 1) in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.
Applications of Integrals | CBSE | Class 12 | Maths | NCERT Exemplar
Draw a rough sketch of the curve y = √(x – 1) in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.

The curve is

\[\begin{array}{*{35}{l}}

y~=\text{ }\surd \left( x~-\text{ }1 \right)  \\

\Rightarrow \text{ }{{y}^{2}}~=\text{ }x\text{ }-\text{ }1  \\

\end{array}\]

Plotting the curve and finding the area of the shaded region between the lines x = 1 and x = 5, we have

NCERT Exemplar Solutions Class 12 Mathematics Chapter 8 - 21
NCERT Exemplar Solutions Class 12 Mathematics Chapter 8 - 22

Therefore, the area of the required region = 16/3 sq.units

i

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