Area Volume

**Kayla_N** · April 24th 2009, 10:06 PM

1. 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.

2. Find the area of the region between

and

for

.
area =????

3. Find the area of the region enclosed between

and

from

to

. Hint: Notice that this region consists of two parts.

Please help and explains..Thanks

**IluvMath** · April 24th 2009, 10:18 PM

Originally Posted by Kayla_N

1. 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.

2. Find the area of the region between

and

for

.
area =????

3. Find the area of the region enclosed between

and

from

to

. Hint: Notice that this region consists of two parts.

Please help and explains..Thanks

1) If you graph the the two equations on a graphing device, you will notice that y = 5x is above y = 6x^2. Hence your integral will be with respect to x integrating (5x - 6x^2)dx between the two point of intersection. The intersection can be found by equation 6x^2 = 5x and solving for x.

2) Use the same method from the previous question but now your limits are from 0 to 1 with respect to x. Remember you are subtracting two areas essentially, so the bottom function which has a smaller area beneath it should be subtracted from the top with a larger area. This technique is easy to employ by again, using a graphing device.

3) Ill leave as an exercise to you hoping that the previous two have helped you

Please message if you need further clarification

**Kayla_N** · April 25th 2009, 12:47 PM

Originally Posted by Kayla_N

1. 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.

2. Find the area of the region between

and

for

.
area =????

3. Find the area of the region enclosed between

and

from

to

. Hint: Notice that this region consists of two parts.

Please help and explains..Thanks

So for number 1, i followed your instruction and graphed and solved for x. X= 0 and 5/6. Now how do i plug it in to find the area??

**e^(i*pi)** · April 25th 2009, 01:11 PM

Originally Posted by Kayla_N

So for number 1, i followed your instruction and graphed and solved for x. X= 0 and 5/6. Now how do i plug it in to find the area??

$\int_0^{\frac{5}{6}} 5x \cdot dx - \int_0^{\frac{5}{6}} 6x^2 \cdot dx$

**IluvMath** · April 25th 2009, 06:19 PM

Originally Posted by e^(i*pi)

$\int_0^{\frac{5}{6}} 5x \cdot dx - \int_0^{\frac{5}{6}} 6x^2 \cdot dx$

There you go some one got there before me :P

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