Question

Find the area bounded under the curve y = 3x² + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.

Answer 1

The given equation of the curve is y = 3x² + 6x + 7.

The area bounded by the curve and the X-axis with coordinates x₁ = 5 and x₂ = 10 is given by
$$\begin{gathered} {\int }_{x_1}^{x_2}ydx \\ ={\int }_5^{10}\left(3x^2+6x+7\right)dx \\ ={\left[\frac{3x^3}{3}+\frac{6x^2}{2}+7x\right]}_5^{10} \\ =1000-125+300-75+70-35 \\ =1370-235 \\ =1135\mathrm{sq}.\mathrm{units} \end{gathered}$$