Question:
Find the area bounded under the curve $y=3 x^{2}+6 x+7$ and the X-axis with the co-ordinates at $x=5$ and $x=10$.
Solution:
$y=3 x^{2}+6 x+7$
Area bounded under the curve within $x=5$ and $x=10$ is calculated by the method of integration.
Area $=\int_{x=0}^{x-\pi} y d x=\int_{x=0}^{x-\pi} \sin x d x=-[\cos \pi-\cos 0]=2$