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

\[\int_{x_1}^{x_2} y dx\]

\[ = \int_5^{10} \left( 3 x^2 + 6x + 7 \right)dx\]

\[ = \left[ \frac{3 x^3}{3} + \frac{6 x^2}{2} + 7x \right]_5^{10} \]

\[ = 1000 - 125 + 300 - 75 + 70 - 35\]

\[ = 1370 - 235\]

= 1135 sq. units