Question

How do you solve this problem? The question is attached as an image. I'm not sure how to break up the function into shapes or elementary figures.

Answer 1

\[\int_{-4}^{5} f(x)dx = \int_{-4}^{-2} f(x)dx +\int_{-2}^{0} f(x)dx + \int_{0}^{5} f(x)dx\]
Now just find teh equation of line AB, BC and CD, then calculate the integral above.

Answer 2

um for the equation of the lines i got -5/2x -1 for BC, 3x+10 for AB, and 2/5x -1 for CD and i got the x-intercepts as -2/5, -10/3 and 5/2

Answer 3

but what exactly are you supposed to do next? i'm kind of new to integrals

Answer 4

check out this nice picture
http://www.wolframalpha.com/input/?i=line+segment+%28-4%2C-2%29%2C%28-2%2C4%29++and+line+segment+%28-2%2C4%29%2C+%280%2C-1%29+and+line+segment+%280%2C-1%29%2C%285%2C1%29

Answer 5

yeah i drew the picture but i was confused as to how to break it up into shapes

Answer 6

Now integrate the equation of line AB from x = -4 to x = -2
Sum with the integral of line BC from x = -2 to x = 0
Sum with the integral of line CD from x = 0 to x = 5

Answer 7

wait how exactly do you find the integral of line BC from x = -2 to x = 0? do you have to break it up into shapes and find the area under and over the line or is there another method?

Answer 8

look up the closed questions from yesterday
asker Math2400
can someone explain how i would go about this?