given y=4x-x^2, need to find area with respect to y axis.

[rowie1600]

hello. need help w/ this one. given y=4x-x^2, need to find area with respect to y axis.. need to change this equation to become a function of x, i.e., y= x+2 becomes x=y-2.. i think i can solve for the area using integration, but cant change the given equation to become function of x.. thanks

 

[Deleted member 4993]

hello. need help w/ this one. given y=4x-x^2, need to find area with respect to y axis.. need to change this equation to become a function of x, i.e., y= x+2 becomes x=y-2.. i think i can solve for the area using integration, but cant change the given equation to become function of x.. thanks

To find area by integration, you'll need to have limits of integration What are the limits of integration?

 

[stapel]

Given y=4x-x^2, need to find [the] area [under the curve?] with respect to [the] y axis. [To start, I] need to change this equation to become a function of x....

Then use what you learned back in algebra: You have a quadratic:

. . . . .$\displaystyle x^2\, -\, 4x\, +\, y\, =\, 0$

Plug into the Quadratic Formula to solve for x in terms of y.

 

[rowie1600]

Thanks for all your help.. There is a graph w/ this problem, but i dont know how to draw it here.. Anyway, the limits are y=0 & y=4.. The graph looks like an inverted arc at the 1st quadrant, with one end passing thru the origin (x=0) and the other at x=4, with the tip of the arc in line with y=4.. The shaded part (the area being solved) is outside the arc, bounded by the + y-axis.. I need to show my solution using integration (thanks for the quadratic equation advice anyway).. Thanks again