Question

I have a question about integrals and solving! I will post the problem below.

Answer 1

@nincompoop

Answer 2

@abb0t

Answer 3

well you can factor out the 7

Answer 4

as it will become

Answer 5

\[\int\limits_{3}^{5} 7(f(x) + 1)dx = 7\int\limits_{3}^{5} (f(x) + 1) dx\]

Answer 6

I figured out that much. I guess I'm just mainly confused on how to solve after that.

Answer 7

@campbell_st

Answer 8

Here are some ways you can break down the left side,\[\large\rm \color{royalblue}{\int\limits_3^5 7f(x)+7~dx}=7\]\[\large\rm \color{royalblue}{\int\limits_3^5 7f(x)dx+\int\limits_3^5 7~dx}=7\]\[\large\rm \color{royalblue}{7\int\limits_3^5 f(x)dx+\int\limits_3^5 7~dx}=7\]

Answer 9

Do you understand how that helps us?

Answer 10

I think so

Answer 11

@zepdrix

Answer 12

You think so? lol :)

Answer 13

I understand how you got those equations, but not sure how to apply them further

Answer 14

Well we're trying to solve for this orange part,\[\large\rm 7\color{orangered}{\int\limits\limits_3^5 f(x)dx}+\int\limits\limits_3^5 7~dx=7\]Just think of this as your "variable" if that helps,\[\large\rm 7\color{orangered}{y}+\int\limits\limits_3^5 7~dx=7\]Solve for y.
That's what the question is asking you to do.

Answer 15

so y = -1 ?

Answer 16

Ah yes, good job! :)

Answer 17

Thank you!