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  4. For the area bounded by the curve y=a x, the line x=2 and x -axis to be 2 sq. units, the value of a must be equal to

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Q. For the area bounded by the curve $y=a x$, the line $x=2$ and $x$ -axis to be 2 sq. units, the value of a must be equal to

Application of Integrals

Solution:

Area $=2=\int\limits_{0}^{2} \text { ax } dx $
$ \Rightarrow 2= a \left[\frac{ x ^{2}}{2}\right]_{0}^{2}$
$ \Rightarrow 2= a \left[\frac{4}{2}-0\right]=2 a$
which gives $a=1$