Need to verify the answer to an integrals question

[Howard]

The area between the functions f(y) = y^2 and g(y) = y + 2 is 14/3. True or false?

(The actual question asks to find the area, but my answer is 14/3).

 

[Howard]

Nobody?

 

[Heisenberg]

What are the integration limits?

 

[Howard]

The points of intersection of the two functions (which I found to be y = -1 and y = 2).

 

[TheLonelyPhoenix]

Give me a min, Diff Eq. has pushed Integral Calc out of my brain...

 

[Heisenberg]

I got 9/2. The integral of f(y) = y^2 is 3 and g(y) = y + 2 is 15/2 for those limits (y= -1 to 2).

 

[TuxDave]

I got 9/2.... maybe I suck...

 

[JetBlack69]

9/2

 

[TuxDave]

Nice... maybe I don't suck at Calc afterall...

 

[JetBlack69]

🙂

 

[JetBlack69]

Oh, to answer your question, false.

 

[TheLonelyPhoenix]

Man, I'm slow... 🙁

 

[MrCodeDude]

I got 8/3

 

[TheLonelyPhoenix]

Originally posted by: MrCodeDude
I got 8/3

Antiderivative of y+2 -> (y^2)/2 + 2y
From -1 to 2:
(2^2/2)+(2*2) - ((-1)^2/2) - (2*-1)
2+4-(1/2)+2
15/2

Antiderivative of y^2 -> (y^3)/3
From -1 to 2:
(2^3/3) - ((-1)^3/3)
8/3 + 1/3
9/3
3

15/2 - 3 = 9/2

 

[BigJ]

9/2

 

[Howard]

Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

 

[Howard]

Originally posted by: TheLonelyPhoenix

Originally posted by: MrCodeDude
I got 8/3

Antiderivative of y+2 -> (y^2)/2 + 2y
From -1 to 2:
(2^2/2)+(2*2) - ((-1)^2/2) - (2*-1)
2+4-(1/2)+2
15/2

Antiderivative of y^2 -> (y^3)/3
From -1 to 2:
(2^3/3) - ((-1)^3/3)
8/3 + 1/3
9/3
3

15/2 - 3 = 9/2

You are supposed to first integrate the boundary functions and then subtract them?

 

[Heisenberg]

Originally posted by: Howard
Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

You can do it that way too. You'll get -9/2 but the sign just depends on the order you subtract them in.

 

[Howard]

Originally posted by: Heisenberg

Originally posted by: Howard
Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

You can do it that way too. You'll get -9/2 but the sign just depends on the order you subtract them in.

Then it's (2^3)/3 - (2^2)/2 - 2(2) - [(-1^3)/3 - (-1^2)/2 - 2(-1)], right?

 

[Heisenberg]

Originally posted by: Howard

Originally posted by: Heisenberg

Originally posted by: Howard
Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

You can do it that way too. You'll get -9/2 but the sign just depends on the order you subtract them in.

Then it's (2^3)/3 - (2^2)/2 - 2(2) - [(-1^3)/3 - (-1^2)/2 - 2(-1)], right?

Yep. You're probably just making an order of operations error somewhere in the calculator or something.

 

[TuxDave]

Originally posted by: Howard

Originally posted by: Heisenberg

Originally posted by: Howard
Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

You can do it that way too. You'll get -9/2 but the sign just depends on the order you subtract them in.

Then it's (2^3)/3 - (2^2)/2 - 2(2) - [(-1)^3/3 - ((-1)^2/2 - 2(-1)], right?

I fixed it a little.

 

[Howard]

Originally posted by: Heisenberg

Originally posted by: Howard

Originally posted by: Heisenberg

Originally posted by: Howard
Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

You can do it that way too. You'll get -9/2 but the sign just depends on the order you subtract them in.

Then it's (2^3)/3 - (2^2)/2 - 2(2) - [(-1^3)/3 - (-1^2)/2 - 2(-1)], right?

Yep. You're probably just making an order of operations error somewhere in the calculator or something.

Damn it.

I just did it on my calculator (integrating the difference of the functions) and now I get -3/2. Fuck!

Tried it again and got -31/6. Wow, I'm so awesome.

 

[Howard]

Originally posted by: Howard

Originally posted by: Heisenberg

Originally posted by: Howard

Originally posted by: Heisenberg

Originally posted by: Howard
Damn... I integrated y^2 - y - 2 from -1 to 2. How did you guys do it?

You can do it that way too. You'll get -9/2 but the sign just depends on the order you subtract them in.

Then it's (2^3)/3 - (2^2)/2 - 2(2) - [(-1^3)/3 - (-1^2)/2 - 2(-1)], right?

Yep. You're probably just making an order of operations error somewhere in the calculator or something.

Damn it.

I just did it on my calculator (integrating the difference of the functions) and now I get -3/2. Fuck!

Tried it again and got -31/6. Wow, I'm so awesome.

Somebody tell me if it's the integral of (y^2 - y - 2) from -1 to 2, please. If that isn't wrong, I don't see how I'm getting -31/6.

 

[Heisenberg]

Originally posted by: Howard
Somebody tell me if it's the integral of (y^2 - y - 2) from -1 to 2, please. If that isn't wrong, I don't see how I'm getting -31/6.

The integral of (y^2 - y - 2) from -1 to 2 is -9/2 according to my TI-89.

 

[Aves]

Originally posted by: Howard
You are supposed to first integrate the boundary functions and then subtract them?

You don't have to do it that way but either way works.