area between two curves (1 Viewer)

[red802]

i got a couple of problems,

can someone show me the working out for these question


1)y=x^2, y =x, x=0 to x=2

2) calculate the area bounded by x = y^2/3 and x=y^2 in the first quadrant

3) find the area bounded by the curves y = x^2, y =x^2

also what would be the next chapter after intergration and also, what does bounded and ecnlosed mean, i know a little but what do they mean

also can u show working out

 

[Trev]

1.
Draw the two graphs, they intersect at (1,1).
The area between the two graphs is therefore:
∫ (x-x²).dx from 0 to 1
plus
∫ (x²-x).dx from 1 to 2
= [x²/2 - x³/3] 0 to 1 + [x³/3 - x²/2] from 1 to 2.
= [1/2 - 1/3 - 0 + 0] + [2³/3 - 2²/2 - 1/3 + 1/2]
= 1 unit²

 

[Riviet]

also what would be the next chapter after intergration and also, what does bounded and ecnlosed mean, i know a little but what do they mean

Schools do the topics in different orders, so it's up to you to ask your maths teacher what topics you'll be doing in the nearby future. Bounded/enclosed means the shaded area between the interesection point(s) of the two curves and the curves themselves.

 

[Trev]

2.
A few ways to do this, but first draw it and find out where the graphs intersect - (1,1) and (0,0).
You could find out the area between each curve and it's closest axis and take it away from the area of the rectangle (1 unit²) or;

∫ (y^2/3-y²).dy from 0 to 1.
[(3/5)y^5/3-(1/3)y³] from 0 to 1.
= 3/5 - 1/3 - 0 + 0
= 4/15 units².

Also, bounded and enclosed is just the area or volume encompassed by the restraints you have been given. It depends on your school/teacher what unit you do next, just ask.