I cannot figure out this question. I really need help from beginning all the way to end.

Let ∫9(bottom) 12 (top) f(x) dx = 9,
∫9 (bottom)10(top) f(x) dx=8,
∫11 (bottom)12(top) f(x)dx = 1.

Find ∫10 (bottom) 11 (top) f(x)dx=

and ∫11 (bottom) 10 (top) (9 f(x)− 8)dx=

2. Originally Posted by derekjonathon
I cannot figure out this question. I really need help from beginning all the way to end.

Let ∫9(bottom) 12 (top) f(x) dx = 9,
∫9 (bottom)10(top) f(x) dx=8,
∫11 (bottom)12(top) f(x)dx = 1.

Find ∫10 (bottom) 11 (top) f(x)dx=

and ∫11 (bottom) 10 (top) (9 f(x)− 8)dx=

If this function is continuous, then the integral from 9 to 12 can be described as the sum of the following integrals:

9 to 10 equals 8
10 to 11 is unknown
11 to 12 equal 1

8 + 1 + unknown = 9

So the integral from 10 to 11 is zero.

For the second part, use the properties of integrals to write it as

9 INTEGRAL(f(x)) - INTEGRAL(8) with bounds as given.

Good luck!!

3. I cant figure out how to calculate the second part...

4. Originally Posted by derekjonathon
I cant figure out how to calculate the second part...
You will need to show a bit more effort. Reviewing the relevant theory in your notes and/or textbook will help.

You have $\int_{11}^{10} (9 f(x) - 8) \, dx$. And you've been told to use the basic properties of integrals. Doing so gives:

$-9 \int^{11}_{10} f(x) \, dx + 8 \int^{11}_{10} \, dx$. Your jobs are:

1. Calculate this.

2. Fill in the steps that led to it.