Question

Find the area enclosed by
y = x and y = x2 in first
quadrant​

Answer 1

Step-by-step explanation:

$First \: we \: find \: the \: cordinates \: of \\ point \: P$

Y = x and y = x²

$⟹ \: x=x </p><p> {}^{2}$

$⟹ x=0,1$

$The\: value \: x=0 \:correspond \: to \: O(0,0).$

$For \: P, x=1</p><p>Now, \: the \: required \: area$

$</p><p>A=∫ </p><p>{0}^{1} </p><p> </p><p> (y </p><p>1</p><p> </p><p> −y </p><p>2</p><p> </p><p> )dx$

$=∫ </p><p> {0}^{1} </p><p> </p><p> (x−x </p><p>2</p><p> )dx \\ </p><p>=[ </p><p> \frac{x {}^{2} }{2} </p><p> </p><p> − \frac{x {}^{3} }{3} </p><p> </p><p> </p><p> ] </p><p> {0}^{1} </p><p> </p><p> \\ </p><p>⟹A= </p><p> \frac{1}{6} </p><p>$