Math Is Fun Forum

amberzak

Member

Registered: 2012-03-16

Posts: 80

Another calculus area Question

The diagram shows the line with equation y=x+1 and the curve with equation y=6x-x^2-3.

The line and the curve intersect at the points A and B, and O is the origin.

a) Calculate the coordinates of A and the coordinates of B.

I've done this:

x+1 = 6x-x^2-3
x=6x-x^2-4
0=5x-x^2-4
x^2-5x+4=0

(x-1)(x-4)

Coordinates are (1,4)

The answer says (1,2) and (4,5) so how do I get the 2 and 5?
Many thanks.

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

Hi amberzak

By solving the equation you get only the x coordinates of the two intersection points. You then substitute those x coordinates into one of those equations to get the y coordinates.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

ahh. thanks

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Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

You're welcome.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

Okay. I've gone wrong again. The next question is to find the area of the shaded area.

So I worked out the quad to have an area of 10.5 (the average of the two sides times the base).

Then I did Funny symbol with top number 4 and bottom number 1   y=6x-x^2-3
=[6x^2 + x^3 -3x] 4,1
    -----     ----
      2         3

=(6X4^2 + 4^3 - 3X4) - (6X1^2 + 1^3 -3X1)
    ---          ---                 -----       ----
     2            3                   2            3

= 32 + 21 1/3 - 12 - 3 + 1/3 - 3
=35 2/3

Minus the Quad = 35 2/3 - 10 1/2
=26 1/6

But the answer says it should be 4.5. So where did I go wrong?

Many thanks

---

Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

You didn't calculate the integral of-x^2 correctly. You changed the sign.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

I'm still not getting the right answer. It's supposed to be 4., apparently, and I'm getting -1. (I don't even know how it's possible to get a minus for area).

Headache

(and thanks for the help)

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Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

Hi

=(6X4^2 + 4^3 - 3X4) - (6X1^2 + 1^3 -3X1)
    ---          ---                 -----       ----
     2            3                   2            3

= 32 + 21 1/3 - 12 - 3 + 1/3 - 3

You haven't changed the sign here!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

THis is what I did.

Why is it not working?

---

Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

The 4th is not correct because you didn't change all of the signs!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

I don't know what you mean. All the signs are negative, so how have I not changed a sign. Can you write it out for me because I can't see why it's wrong.

---

Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

Stay online while I type it out.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

Here is the solution to the integral:

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

Why are they plus? I'm sure it's a very simple reason, and I've probably been staring at the problem for too long to see it.

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Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

Isn't -(-a)=a?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

amberzak

Member

Registered: 2012-03-16

Posts: 80

Re: Another calculus area Question

Yeah. See, I knew it was simple. Been staring at the problem too long.

Thanks

---

Don't think outside the box. Think there is no box

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Another calculus area Question

You're welcome.Does that give you the right answer?It should.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.