MATH
posted by AIRA .
Region A that on xyplane is bounded by two (2) curves and a line. The curves are y=x^32x+3 and y=x^2+3 while the line is x=0. It is located in the first quadrant of xyplane. Determine the area of region A.

Make a sketch and then solve for the intersection of the two curves
x^2  2x + 3 = x^2 + 3
.....
x = 0 or x = 1
so
area = [integral] (x^2 + 3 (x^2  2x+3)) dx from 0 to 1
= integral (2x^2 + 2x)dx from 0 to 1
= (2/3)x^3 + x^2  from 0 to 1
= 2/3 + 1  0
= 1/3
Respond to this Question
Similar Questions

Calc Jacobian
Thanks "I know that the xy region is the line x=y y=0 and y=1 x/2)" It is helpful to rewrite the region in the xy plane by specifying the three lines and the endpoints, i.e. the points where they intersect. If you insert these points … 
calculus
Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the xaxis; 3) Find the volume of the … 
Calculus (Area Between Curves)
Find the area of the region bounded by the curves y^2=x, y4=x, y=2 and y=1 (Hint: You'll definitely have to sketch this one on paper first.) You get: a.) 27/2 b.) 22/3 c.) 33/2 d.) 34/3 e.) 14 
Calculus (Area Between Curves)
Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=44x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859 Based on my calculations, I … 
Calculus (Area Between Curves)
Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=44x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859 
calculus
Consider the curves y = x^2and y = mx, where m is some positive constant. No matter what positive constant m is, the two curves enclose a region in the first quadrant.Without using a calculator, find the positive constant m such that … 
geometry
Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless … 
geometry
Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless … 
math
Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless … 
calculus review please help!
1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the …