Question

Let f(x) be defined by f(x) = x if x 0. the value of the integral from -2 to 1 of xf(x)dx =
a.3/2
b.5/2
c.3
d. 7/2
e. 11/2

Answer 1

\[\int\limits_{-2}^{1} xf(x)dx\]

Answer 2

basically the pieces
\[x, x \le 0\]
\[x+1, x > 0\]

Answer 3

i think you supposed to break it up?
\[\int\limits_{1}^{1} x(x+1)dx\] = 0
\[\int\limits_{0}^{-2} x^2dx\] = -8/3
i'm doing something wrong...

Answer 4

Limits of integration should be [-2,0] and [0,1] respectively.

Answer 5

ohhh that's what i thought but cuz it's not greater than or equal to, i didn't put the zero...

Answer 6

Also, for the first part you seem to have taken the integral from 0 to -2. It should be from -2 to 0.

Answer 7

oops my bad.

Answer 8

ok yeah thanks. i got 7/2 as the answer

Answer 9

That's what I got too.

Answer 10

k thanks.

Answer 11

\[\int\limits\limits_{1}^{1} x(x+1)dx \]Looks like you got this already, but as for this part with the limits of integration that you were confused on - you can still pick the first limit on the integral as 0, even though the function is defined as x>0.

The picture might help. Even though x>0, the area under the curve is still effectively from x=0 to x=1. If you only integrate from 1 to 1, the area under that is zero. You could pick a value of x just slightly greater than x=0, like 0.0000000000001, and do the integration, and you'll get essentially the same amount for the area from x=0.0000000000001 to x=1 as you do for x=0 to x=1.

Sorry if that sounded confusing..