Help

[akaku]

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
2y=4x , y=3 and 2y+4x=8

 

[Deleted member 4993]

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
2y=4x , y=3 and 2y+4x=8

Please share your work with us, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[akaku]

i sketched the graphs but i don't know what area to take because all three graphs intersect at x=2 so there is no enclosed space to take the area

 

[BigGlenntheHeavy]

\(\displaystyle Here \ is \ the \ graph, \ I \ assume \ you \ can \ take \ it \ from \ here.\)

[attachment=0:3fu4lfko]xyz.jpg[/attachment:3fu4lfko]

 

[Deleted member 4993]

i sketched the graphs but i don't know what area to take because all three graphs intersect at x=2 so there is no enclosed space to take the area

the lines 2y = 4x and 2y + 4x = 8 intersect at (1, 2) i.e. x =1 and y =2

the lines 2y = 4x and y =3 intersect at (3/2, 3) i.e. x =3/2 and y =3

the lines 2y + 4x = 8 and y =3 intersect at (1/2, 3) i.e. x = 1/2 and y =3

as shown in the graph drawn by Glenn (above).

In these types of problems - use your graphing calculator - and sketch the situation.