Question

Find the area of the region enclosed by the curves x = 5y2, x = 0, and y = 1. The area of the region enclosed by the curves is (Type a simplified fraction.)

Answer 1

I am attaching the pictures of solution. If you find my answer helpful please press thumbs up button. Thanks.

Region is bounded by x=54², x=0 and y=). x=sy is equation of pasabola. x=542 Ix standard form of equation of parabola is 4² - 4ax at y=0, x=542 )=sloo = x=0 x=54e passes through So point At x=5, (0,0). x=sye =) 5=59 2

- 4 = 5/5 =) = y =) =) y = 11 So x=54² bosses through points (5,1) and (5,-1). Using these points we draw curve x=sye / 19 4x=59 (0) S Now Y=l is lene parallel to x-axis passing through boint (0,1).

(as y=( is line baralle to x-axis bassing through point 10,() .. And x=0 is y-axis. So our region will be follows:

y=1 x=o x=542 x (0,0) yao Joo 28t оbtа театъ, we will draw horizontal strip. Now limits of x will be: - to as left end of stres touches and right end of strip touches x=542 хо x- 5y2 * -o

Now limits of y will be an y=o to as strip can y=1 move between y =o (from below) to y =) (above) sg sy dx dy 11 y=0 x=0 (by O &@) s' y=0 Sdx=x s (syd-dd dy becau cause o

- area= area=s syddy - 5 y=0 2+1 55 = ly 2+1 because syn dy = you n+1 mti where n&(-1) $(3)). - area = 5 3