A curve $$y=f(x)$$ which passes through (4$$,$$0) satisfies the differential equation $$xdy+2ydx=x(x$$−$$3)dx$$ . The area bounded by $$y=f(x)$$ and line $$y=x$$ (in$$ square $$unit) is

Question

A curve $$y=f(x)$$ which passes through (4$$,$$0) satisfies the differential equation $$xdy+2ydx=x(x$$−$$3)dx$$ . The area bounded by $$y=f(x)$$ and line $$y=x$$ (in$$ square $$unit) is

Infinity Learn · Accepted Answer

$$xdy+2ydx=x(x$$−$$3)dx$$⇒$$x2dy+2xydx=x3$$−$$3x2dx$$⇒$$dx2y=x3$$−$$3x2dx$$⇒$$yx2=x44$$−$$x3+cCurve$$ passes through the point (4$$,$$0). ∴$$c=0$$ Therefore, curve is $$y=x24$$−x and point of intersection of $$y=x$$ and this curve is $$x=x24$$−x   ⇒$$8x-x2=0$$  ⇒$$x=0$$, $$x=8$$ Required area $$=$$∫$$08$$ x−$$x24$$−$$xdx=x2$$−$$x31208=64$$−$$23$$×$$64=643$$

$A curve y = f (x) which passes through (4, 0) satisfies the differential equation$
$x d y + 2 y d x = x (x - 3) d x . The area bounded by y = f (x) and line y = x (in square unit) is$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A curve y=f(x) which passes through (4,0) satisfies the differential equation xdy+2ydx=x(x−3)dx . The area bounded by y=f(x) and line y=x (in square unit) is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$A curve y = f (x) which passes through (4, 0) satisfies the differential equation$
$x d y + 2 y d x = x (x - 3) d x . The area bounded by y = f (x) and line y = x (in square unit) is$