math
posted by Saima .
Find the area of the region enclosed:
Y=x3+5x2+3, y=x2+7x +3,
X=0,x=3

We must first find where the two curves intersect.
x^3 + 5x^2 + 3 = x^2 + 7x + 3
x^3 + 4x^2  7x = 0
x(x^2 + 4x  7)=0
so x=0 or x = 2 ± √11
so there is an intersection between our domain of x=0 to x=3 , this makes it quite messy.
We have to split the area into two regions
one from 0 to 2+√11
another from 2+√11 to 3
In the first region, the parabola is above the cubic, so the effective height is (x^2+7x+3)  (x^3 + 5x^2 + 3)
= x^3  4x^2 + 7x
while for the second region the height will be
x^3 + 4x^2  7x
So Area
= integral[x^3  4x^2 + 7x] from 0 to 2+√11 + integral[x^3 + 4x^2  7x] from 2+√11 to 3
= [(1/4)x^4  (4/3)x^3 + (7/2)x ] from 0 to 2+√11 + [(1/4)x^4 + (4/3)x^3  (7/2)x ]from 2+√11 to 3
I will let you do the messy arithmetic,
Good Luck.
Respond to this Question
Similar Questions

calculus
find the value of m so that the line y = mx divides the region enclosed by y = 2xx^2 and the xaxis into two regions with equal area i know that the area enclosed by y=2xx^2 is 4/3 so half of that would be 2/3 however, i have no … 
Math Calc
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=e^(4x), y=e^(6x), x=1 
precalc
area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three parallel … 
calculus
the region enclosed by 2y=5xy=5 and 2y+3x=8. Decide whether to integrate with respect to x or y, and then find the area of the region. The area is 
math
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=e^1x, y=e^4x, x=1 
Calculus
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 = 4(x^(1/2)), y=4, and 2y +2x = 6 I keep getting an area around 21.3 but it is incorrect. Am I … 
math
A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas. If the total enclosed area is 225 ft2, find the dimensions of the enclosed region. 
math
A rancher wishes to use 86 ft of fencing to enclose a rectangular paddock and subdivide the region into three smaller areas. If the total enclosed area is 225 ft2, find the dimensions of the enclosed region. 
math
Roughly sketch the region enclosed by the curves y = sin x, y = cos x and the x  axis between x = 0 and x = p/ 2 . Also find the area of this region. 
calculus
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=3+√X, y=3+1/5x What is the area?