Question

How do I do this?

Answer 1

\[\int\limits_{0}^{9}f(x)dx=37; \int\limits_{0}^{9}g(x)dx=16\]

Answer 2

Find:
\[\int\limits_{0}^{9}[2f(x)+3g(x)]dx\]

Answer 3

the integral is "linear"

in other words, for a constant "a"
\[ \int\limits_{0}^{9} a f(x)dx = a\int\limits_{0}^{9} f(x)dx \]

Answer 4

so in this case \[2\int\limits_{0}^{9} x.dx\]??

Answer 5

and you can separate integrals (assuming they have the same limits
\[ \int\limits_{0}^{9} f(x) + g(x) dx= \int\limits_{0}^{9} f(x)dx + \int\limits_{0}^{9} g(x)dx\]

Answer 6

not x , f(x)
so separate the problem into
\[ 2\int\limits_{0}^{9} f(x)dx + 3\int\limits_{0}^{9} g(x)dx \]

Answer 7

yea right! so \[37x(9,0)+16x(9,0)\]

Answer 8

I don't know about the x(9,0) part

just replace the integral with the number they say it is equal to
\[ 2\cancel{(\int\limits_{0}^{9} f(x)dx)}37 + 3\int\limits_{0}^{9} g(x)dx \]
and do the same for the other, it is 16

Answer 9

I am trying to show you sub in 37 for the result of the first integral

Answer 10

ohh alright, i got it!

Answer 11

so its 2(37) + 3(16)
= 122

Answer 12

thanks @phi :)