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Question

# â€‹The area of the bounded by the curve y2 = x, line y = 4 and y-axis is _________________.

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Solution

## To find: area of the region bounded by the curve y2 = x, line y = 4 and y-axis The required area of the region = ${âˆ«}_{0}^{4}xdy$ Thus, $\mathrm{Required}\mathrm{area}={âˆ«}_{0}^{4}xdy\phantom{\rule{0ex}{0ex}}={âˆ«}_{0}^{4}{y}^{2}dy\phantom{\rule{0ex}{0ex}}={\left(\frac{{y}^{3}}{3}\right)}_{0}^{4}\phantom{\rule{0ex}{0ex}}=\left(\frac{{4}^{3}}{3}\right)-\left(\frac{{0}^{3}}{3}\right)\phantom{\rule{0ex}{0ex}}=\frac{64}{3}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{Area}=\frac{64}{3}\mathrm{sq}.\mathrm{units}$ Hence, the area of the region bounded by the curve y2 = x, line y = 4 and y-axis is $\overline{)\frac{64}{3}\mathrm{sq}.\mathrm{units}}.$

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