Question

Find the area bounded by the curve



y =x²

with X-axis from x=0 to x=2​

Answer 1

${\orange{ \boxed{ \boxed{ \begin{array}{cc} \bf \to \: given \: : \: \\ \\ \rm \: the \: equation \: of \: curve \: , \: y = {x}^{2} \\ \\ \rm \: area \: bounded \: by \: x - axis \: from \: \\ \rm \: x = 0 \: to \: x = 2 \\ \\ \\ \rm \: area = \displaystyle \int_0 ^{2} \: \rm \: y \: dx \\ \\ \rm =\displaystyle \int_0 ^{2} \: \rm \: {x}^{2} \: dx \\ \\ \rm = { \huge{[ }}\frac{ {x}^{3} }{3}{ \huge{]}}_0 ^{2} \\ \\ \rm = \frac{ {2}^{3} }{3} - 0 \\ \\ = \frac{8}{3} \: \sf{unit}^{2} \end{array}}}}}$