Evaluating Integrals: Additive Interval Property

[mathpat]

Homework Statement

Given
7 f(x) dx= 8
0

7 f(x) dx = −3
1

evaluate the following.

1 f(x) dx
0

Homework Equations

n/a

The Attempt at a Solution

I'm a little confused on how to approach this problem. Do i use the additive interval property of integrals?

 

[Mark44]

Homework Statement

Given
7 f(x) dx= 8
0

7 f(x) dx = −3
1

evaluate the following.

1 f(x) dx
0

Homework Equations

n/a

The Attempt at a Solution

I'm a little confused on how to approach this problem. Do i use the additive interval property of integrals?

Yes.

 

[mathpat]

I ended up with 5. Is that correct?

 

[Mark44]

I ended up with 5. Is that correct?

So 5 + (-3) = 8?

 

[UVW]

To expand on what Mark44 is saying, remember that these integrals represent areas under your curve, f(x). If you know how much area is under the curve between x = 0 and x = 7 and also know how much area is under the curve between x = 1 and x = 7, can you intuitively decide how to find the area between x = 0 and x = 1?

 

[mathpat]

Yea I understand but when I use the formula i keep getting 5. I don't see where I'm going wrong.

 

[Infrared]

\int_0^7 f(x) dx = \int_0^1 f(x) dx + \int_1^7 f(x) dx. What happens when you plug in what you know?

 

[mathpat]

I calculated 11 using that formula.

 

[Infrared]

Good, that's right.

 

[mathpat]

Thanks