A rectangular room is 11 feet by 16 feet. The ceilings are 8 feet high. If a gallon of paint covers 50 square feet. Fill in the following blanks.

Solved

Show answers

Ответ:

myahr159

26.05.2020

Mathematics

Step-by-step explanation:

From your problem, we have to extract the information that are important from the first two intregrals so we can solve the double integral.

$\int\limits^{-1}_{-4} {f(x)} \, dx = 0$

We also have that:

$\int\limits^{3}_{1} {g(x)} \, dx = 3$

---------------------------------

With this, now we can solve the double integral.

Since the limits of integration are constant, i can use dA both as dydx or dxdy. I am going to use dydx.

So the double integral will be:

$\int \limits^{-1}_{-4} \int \limits^{3}_{1} {g(y)} {f(x)} dy dx\$

We solve a double integral from the inside to the outside, so the first integral we solve is:

$\int \limits^{3}_{1} \y g(y) \x f(x) dy$

f is a function of x and we are integrating dy, so this means that f is a constant. Our integral now is this:

$\x f(x) \int \limits^{3}_{1} \y g(y) dy$

From above, we have that

$\int \limits^{3}_{1} \x g(x) dx = 3$

So,

$\int \limits^{3}_{1} \y g(y) dy = 3$

Now we have to solve the outside integral:

$3\int\limits^{-1}_{-4} {f(x)} \, dx$

We know that

$\int\limits^{-1}_{-4} {f(x)} \, dx = 0$

So the double integral will be 0

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice