Question

True or False.

Answer 1

If \[\int\limits_{0}^{2}f(x)dx = 6\] then \[\int\limits_{0}^{4}f(x)dx =12\]

Answer 2

@amistre64

Answer 3

not in general

Answer 4

\[\int\limits_{0}^{2}f(x)dx = \int\limits_{0}^{2}f(t)dt\]

Answer 5

in general, the integration of 2 functions are not equal ....

Answer 6

\[\int\limits_{-1}^{1}f(x)dx = 2\int\limits_{0}^{1}f(x)d\]

Answer 7

only if a function is even i beleive

Answer 8

The question only has that as a statement with the option of either true or false. I believe it is false because they haven't stated it as even.

Answer 9

\[\int_{-1}^{1}x~dx=\frac12(1)^2-\frac12(-1)^2=0\]

Answer 10

\[\int_{0}^{1}x~dx=\frac12(1)^2-\frac12(0)^2=\frac12\]
and 2*1/2 not equal 0

Answer 11

Okay, thank you for that. It really helped to look at it that way.

Answer 12

when in doubt, run a simple test :)