Are My Basic Integration Answers Correct?

[t_n_p]

Just double checking my answers basically, its been a while since I did this..

http://img220.imageshack.us/img220/4075/65177751rq6.jpg

My answer is 14

http://img220.imageshack.us/img220/3291/92105764te4.jpg

My answer is -22

http://img223.imageshack.us/img223/4874/13030647ds3.jpg

My answer is 23

http://img223.imageshack.us/img223/5766/95610620ke0.jpg

My answer is 4

Hope I'm right!

 

[siddharth]

Your images don't seem to be loading in my comp, although I don't know if it loads for others. Maybe you can try posting the questions in LaTeX?

 

[t_n_p]

Your images don't seem to be loading in my comp, although I don't know if it loads for others. Maybe you can try posting the questions in LaTeX?

hope you can see them now!

 

[christianjb]

Your last answer is wrong

|10-3|=|7|=7

 

[t_n_p]

Your last answer is wrong

|10-3|=|7|=7

Dammnit, that means I got Q1 wrong too. I just double checked, the area labelled 3 refers to the interval from b to c.

 

[Gib Z]

No t_n_p you are correct! christianjb didn't look at the bounds close enough!

However for question 2 we can rewrite as $-2\int^c_a f(x) dx$. The integral can be seen to be 6-17=-11. Then times by -2. 22, not negative 22.

 

[t_n_p]

No t_n_p you are correct! christianjb didn't look at the bounds close enough!

However for question 2 we can rewrite as $-2\int^c_a f(x) dx$. The integral can be seen to be 6-17=-11. Then times by -2. 22, not negative 22.

Are you sure?
Re Q1, 10-3+10=17?

Re Q4, 10-3 = 7?

 

[Gib Z]

Well I'm assuming the area labelled 3 in both the diagrams refers to the area between c and the origin, not c and b..

 

[t_n_p]

Well I'm assuming the area labelled 3 in both the diagrams refers to the area between c and the origin, not c and b..

Sigh, yeh, 3 refers to interval between c and d.

So I've got 1/4 right.

 

[Gib Z]

1. 17
2. 22
3. 23
4. 7

Any confusions just ask.

And sorry about that christianjb, I guess I jumped the gun.

 

[HallsofIvy]

No one seems to have mentioned problem 1, which seems quite easy, but your given answer, 14, is clearly wrong. In fact, I'm wondering where you could have got that! You are told that the area under the curve on the right is 10. You are also told that the function is even so the curve is symmetric about the y-axis and therefore the area under the curve on the left is also 10. Finally, you are told that the area above that small part in the middle is 3. Because it is below the x-axis the integral itself is negative. The total area is, of course, the sum of the "positive" areas minus the negative "area". And that is not 14!

Did you perhaps think that the portion, below the x-axis, to the right of the y-axis was 3? That would make the total "negative" area 6 and would give a total of 10+10- 6= 14 for the total area. That is not, however, how I would interpret what is given.

 

[t_n_p]

No one seems to have mentioned problem 1, which seems quite easy, but your given answer, 14, is clearly wrong. In fact, I'm wondering where you could have got that! You are told that the area under the curve on the right is 10. You are also told that the function is even so the curve is symmetric about the y-axis and therefore the area under the curve on the left is also 10. Finally, you are told that the area above that small part in the middle is 3. Because it is below the x-axis the integral itself is negative. The total area is, of course, the sum of the "positive" areas minus the negative "area". And that is not 14!

Did you perhaps think that the portion, below the x-axis, to the right of the y-axis was 3? That would make the total "negative" area 6 and would give a total of 10+10- 6= 14 for the total area. That is not, however, how I would interpret what is given.

Yeah that's what I did in Q1 and 4. I just assumed 3 was from 0 to c, but I've now been told that its from b to c.

 

[HallsofIvy]

The question is WHO told you that? That would be my interpretation but it is your teacher's that is important!

 

[t_n_p]

The question is WHO told you that? That would be my interpretation but it is your teacher's that is important!

Unfortunately, the teacher told me that...

 

[christianjb]

1. 17
2. 22
3. 23
4. 7

Any confusions just ask.

And sorry about that christianjb, I guess I jumped the gun.

Aha, I best the mighty Gib Z in integral combat at last!

 

[HallsofIvy]

Unfortunately, the teacher told me that...

Not "unfortunately"! That's exactly who has the right to tell you that!

 

[t_n_p]

Not "unfortunately"! That's exactly who has the right to tell you that!

Well it was unfortunate for me...

 

[TheoMcCloskey]

And (unless I'm missing something) no-one seems to have noticed that the limits of the integral in Q1 are from "d" to "a" and not from "a" to "d" as one might expect.

Hence, the value of the integral is actually -(10 -3 + 10) = -17.

 

[Gib Z]

::Cries:: Good spot Theo I am having a really bad episode..