Find the area bounded by the curve y = $3 x^{2}$ +6x+7 and the X-axis with the x=5 and x=10.

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Solution

Given, Area bounded by the curve, x axis with coordinates

x= 5 and

x= 10 is given by,

Area = $\int_{x_{1}}^{x_{2}}$ y dx

= $\int_{5}^{10} (3 x^{2} + 6 x + 7) d x$

= ${[\frac{3 x^{3}}{3} + \frac{6 x^{2}}{2} + 7 x]}_{5}^{10}$

= 1000-125+300-75+70-35

= 1370-235

= 1135 sq units.

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y = 3 x^{2} + 6 x + 7

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