Question

Final question for me.
See graph attached

Answer 1

Let g(x) = \[\int\limits_{0}^{x}f(x)dx\]

Find: \[\int\limits_{0}^{5}f(x)dx\]

Answer 2

Why not just use triangles and rectangles to get the area under the function?

Answer 3

I have thought of breaking it into three parts
finding the area from 0 to 2, 2 to 4 and 4 to 5
is this right?

Answer 4

x=4->x=5 is a rectangle

Answer 5

\[\int^5_0 f(x) dx = 2*1/2+3*2/2+1*3=1+3+3=7\]

Correct @afternoonmrmoon

Answer 6

Triangle = B*H/2, Rectangle=L*W

Answer 7

x=2->4 is a right triangle as is x=0->2

Answer 8

zed could you explain what you did there
its hard to see what you wrote.

Answer 9

ah I see what you did

Answer 10

That makes much more sense
Thanks Zed. :)
one quick question if I wanted to find the integral of g"(x) would that be just the integral of g'(x)?

Answer 11

\[\int g''(x) dx=g'(x)+C\]

Answer 12

Thanks a bunch :)