Question

i have no idea how to do this at all -_-

Answer 1

\[\int_a^b f(x)dx=\int_a^cf(x)dx+\int_c^b f(x)dx\]

Answer 2

you would like to have
\[\int_0^3f(x)dx=\int_0^1f(x)dx+\int_1^3f(x)dx\] but you donot have the first one
\[\int_0^1f(x)dx\] but rather you have
\[\int_{-1}^1f(x)dx\]

Answer 3

on the other hand from the picture you can see that
\[\int_{-1}^1f(x)dx=2\int_0^1f(x)dx\] and so
\[\int_0^1f(x)dx=\frac{1}{2}\int_0^1f(x)dx\]

Answer 4

sorry last line should have been
\[\int_0^1f(x)dx=\frac{1}{2}\int_{-1}^1f(x)dx\]

Answer 5

but the answers asking for 0 to 3?

Answer 6

right
\[\int_0^3f(x)dx=\int_0^1f(x)dx+\int_1^3f(x)dx=\frac{1}{2}\int_{-1}^1f(x)dx+\int_1^3f(x)dx\]

Answer 7

that was the gimmick to recognize that the part you want \(\int_0^1f(x)dx=\frac{1}{2}\int_{-1}^1f(x)dx\) so you could use that instead

Answer 8

since they called \(\int_{-1}^1f(x)dx=A\) and \(\int_1^3f(x)dx=B\) your want to write
\[\int_0^3f(x)dx=\frac{1}{2}A+B\]

Answer 9

thank u ima run thru it and make sure i get it again

Answer 10

ok i think i wrote it all out