# calculus

posted by .

find the area the region bounded by the graphs of the given equation y=81x,y=x^5,x=0,x=3

• calculus -

The area is between the function y=x^5 and y=81x, between the limits x=0 and x=3.

The functions are all in the first quadrant (no values negative), and the two curves y=81x and y=x^5 intersect at x=3, the upper integration limit, which is a "lucky coincidence".

The area function a(x), is therefore
a(x)=81x-x^5
You would integrate a(x) from 0 to 3 to find the area, thus
Area = ∫a(x)dx [x=0,3]
=∫(81x-x^5)dx [x=0,3]

Here's an image to give you an idea of the area:
http://img11.imageshack.us/img11/6060/1290966183.png

## Similar Questions

1. ### calculus

Find the area of the region bounded by the graphs f(x)=sqrt(3x)+1, g(x)=x+1
2. ### calculus

Sketch the region bounded by the graphs of the algebraic functions & find the area of the region: f(x)=10/x, x=0 , y=2, y=10 I started idk how to keep going y = 10/x for x -->x = 10/y
3. ### calculus

FInd the area of the region bounded by the graphs of y= 3x^2+1 , y=0, x=-2.7, x=2.5
4. ### calculus

find the volume of the solid bounded above by the surface z=f(x,y) and below by the plane region R f(x,y)=2x^2 y;R is the region bounded by the graphs of y=x and y=x^2
5. ### calculus

1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral. 2. Find the area of the region bounded by x=y^2+6, x=0 , y=-6, and y=7. Show …
6. ### Calculus AP

Let R be the region bounded by the graphs of y=cos((pi x)/2) and y=x^2-(26/5)x+1. A. Find the area of R. B. The vertical line x=k splits the region R into two equal parts. Write, but do not solve, an equation involving integrals that …
7. ### Calculus

Find the area of the region bounded by the graphs of the given equations: y=x, y=2√x
8. ### Calculus

How do I find the area of the region bounded by the graphs of the given equations?
9. ### Calculus

find the area of the region bounded by the graphs of y=-x^2+5x+2 and y=2
10. ### Calculus

find the area of the region bounded by the graphs of y=x^2 and y=cos(x)

More Similar Questions