Thread: pre-calculus questions

I have an online quiz, that I am currently taking and should submit pretty soon.
The answer in bold is the one I chose. If I am wrong, please explain why
Thanks for any input, I appreciate it.
---

1) Let R be the region between the curves y=x^2
and y=2x-(x^2).

To find the area of R, we need to

A) integrate [(x^2)-(2x-x^2)] from 0 to 1
B) integrate [(2x-x^2)-(x^2)] from 0 to 1
C) integrate [(x^2)-(2x-x^2)] from 0 to 2
D) integrate [(2x-x^2)-(x^2)] from 0 to 2


2)Let R be the region bounded by the curves y=(x^2)+3 and y=x, for x in [-1,1].


The area of R is equal to

A) 2
B) 17/3
C) 20/3


3) Let R be the region bounded by the curves x=(y^2) and y=x+5, for y in [-1,2].

Sketch the region, then answer the following question.

The most convenient way to find the area of R is to slice the region...

A) horizontally
B) vertically

Originally Posted by daneeyah

I have an online quiz, that I am currently taking and should submit pretty soon.
The answer in bold is the one I chose. If I am wrong, please explain why
Thanks for any input, I appreciate it.
---

1) Let R be the region between the curves y=x^2
and y=2x-(x^2).

To find the area of R, we need to

A) integrate [(x^2)-(2x-x^2)] from 0 to 1
B) integrate [(2x-x^2)-(x^2)] from 0 to 1
C) integrate [(x^2)-(2x-x^2)] from 0 to 2
D) integrate [(2x-x^2)-(x^2)] from 0 to 2

correct

Thank you I appreciate it

What about the other two?
I am pretty sure #2 is correct, but #3 I am a bit unsure about.
Thanks again for your time, I appreciate it.

Originally Posted by daneeyah

2)Let R be the region bounded by the curves y=(x^2)+3 and y=x, for x in [-1,1].


The area of R is equal to

A) 2
B) 17/3
C) 20/3

yes

Originally Posted by daneeyah

3) Let R be the region bounded by the curves x=(y^2) and y=x+5, for y in [-1,2].

Sketch the region, then answer the following question.

The most convenient way to find the area of R is to slice the region...

A) horizontally
B) vertically

no. did you graph it?

it is almost obvious from the graph that the best way to find the area here is to write both functions in terms of y and do the required integral. in that case, we need rectangles whose lengths are parallel to the x-axis (you need to know how we define the integral based on Riemann sums to know what rectangles we are talking about here)

Originally Posted by Jhevon

no. did you graph it?

it is almost obvious from the graph that the best way to find the area here is to write both functions in terms of y and do the required integral. in that case, we need rectangles whose lengths are parallel to the x-axis (you need to know how we define the integral based on Riemann sums to know what rectangles we are talking about here)

I just graphed it again.. I see how horizontal would be better.
Thanks again.. I just submitted my quiz and got a 100.

Originally Posted by daneeyah

I have an online quiz, that I am currently taking and should submit pretty soon.
The answer in bold is the one I chose. If I am wrong, please explain why
Thanks for any input, I appreciate it.
---

1) Let R be the region between the curves y=x^2
and y=2x-(x^2).

To find the area of R, we need to

A) integrate [(x^2)-(2x-x^2)] from 0 to 1
B) integrate [(2x-x^2)-(x^2)] from 0 to 1 Mr F says: Correct.
C) integrate [(x^2)-(2x-x^2)] from 0 to 2
D) integrate [(2x-x^2)-(x^2)] from 0 to 2


2)Let R be the region bounded by the curves y=(x^2)+3 and y=x, for x in [-1,1].


The area of R is equal to

A) 2
B) 17/3
C) 20/3 Mr F says: Correct.


3) Let R be the region bounded by the curves x=(y^2) and y=x+5, for y in [-1,2].

Sketch the region, then answer the following question.

The most convenient way to find the area of R is to slice the region...

A) horizontally
B) vertically Mr F says: Horizontal is most convenient for me. But you know what they say .... one man's meat is another man's poison ..... I think the question is quite stupid, actually.

..

Originally Posted by daneeyah

I just graphed it again.. I see how horizontal would be better.
Thanks again..

you're welcome

I just submitted my quiz and got a 100.

very nice!

Originally Posted by Jhevon

you're welcome

very nice!

Yes, well done Jhevon!