Homework Help: MATH

Posted by AIRA on Thursday, April 7, 2011 at 2:55am.

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

MATH - Reiny, Thursday, April 7, 2011 at 8:18am
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

Answer this Question

Related Questions

Calc Jacobian - Thanks "I know that the xy region is the line x=y y=0 and y...
calculus - Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find ...
Calculus [rotation of region bounded by curves] - Find the volume of the solid ...
Math Calc 1 Last question - Find the volume of the solid obtained by rotating ...
calculus - Find the number b such that the line y = b divides the region bounded...
calculus - Find the number b such that the line y = b divides the region bounded...
calculus - Consider the curves y = x^2and y = mx, where m is some positive ...
calculus - Find the volume of the solid obtained by rotating the region bounded ...
Calculus - 1. Find the area of the region bounded by the curves and lines y=e^x ...
cal 2 - Find the number b such that the line y = b divides the region bounded by...

For Further Reading

First Name:
School Subject:
Answer: