## Andresfon12 3 years ago find the volume of the given solid: under the plane x+2y-z=0, and above the region bounded by y=x and y x^4

1. TuringTest

where are you stuck?

2. Andresfon12

find the value for x

3. Andresfon12

finding*

4. TuringTest

where do the graphs of y=x and y=x^4 intersect?

5. Andresfon12

at 1?@TuringTest

6. TuringTest

that's one of the intersection points, yes and the other?

7. Andresfon12

16

8. Andresfon12

|dw:1360707284131:dw|

9. TuringTest

x=16 is not an intersection, set the two equations equal and solve:$x=x^4$$x^4-x=0$$x^3(x-1)=0$so the intersections are x=1 and x=?

10. TuringTest

typo, should be$x^4=x$$x^4-x=0$$x(x^3-1)=0$

11. Andresfon12

-1 to 1

12. TuringTest

$x(x^3-1)=0\implies x=0\text{ or }x^3-1=0\implies x=1$so$x=\{0,1\}$try drawing the graphs out if you doubt that