Question

Please give the answer with complete explanation in order to get the BRAINLIEST tag :)​

Answer 1

Answer:

$\boxed{\mathfrak{Area \ of \ the \ shaded \ part = 72}}$

Given:

y = x²

$\sf x_1 = 0$

$\sf x_2 = 6$

Explanation:

$\rm Area \: under \: curve = \int\limits^{x_2}_{x_1} y.dx \\ \\ \rm = \int\limits^{6}_{0} {x}^{2} .dx \\ \\ \rm = \dfrac{ {x}^{3} }{3} \Big|_0^6 \\ \\ \rm = \dfrac{( {6}^{3} - {0}^{3} )}{3} \\ \\ \rm = \dfrac{ 216 }{3} \\ \\ \rm =72$

Note: If equation of curve is given we need to integrate that equation for finding area under curve.