Please help, its urgent :(

Question

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.
y=3x, y=5x^2

Answer 1

Hi, Angie. I assume you have a graphing calculator or can use the one at http://www.coolmath.com/graphit/index.html to plot the two functions.

 

The enclosed region is a small sliver bound by where the curves intersect at the origin and (0.6,1.8).

 

Whether to integrate with respect to x or y depends on which integral you'd rather do.

 

Integrating wrt x: A=∫(f2(x)-f1(x))dx=∫(3x - 5x^2)dx (from 0 to 0.6)

 

Integrating wrt y: A=∫(g2(y)-g1(y))dy=∫(√5 y - √(3y))dy (from 0 to 1.8)

 

Neither of these is THAT daunting, although I'll take the polynomial with integral coefficients over the one with fractional coefficients any day!

 

Continuing the integration wrt x:

A=3/2 x^2 - 5/3 x^3 (from 0 to 0.6)=3/2 (0.6)^2 - 5/3 (0.6)^3=0.18