# Let f(x)=0 if x is less than -4 3 if x is greater than or equal to -4 and less than -1 -4 if x is greater than or equal to -1 and less than 4 0 if x is greater than or equal to 4 and g(x)=...

Let f(x)=

0 if x is less than -4

3 if x is greater than or equal to -4 and less than -1

-4 if x is greater than or equal to -1 and less than 4

0 if x is greater than or equal to 4

and g(x)= integrate from -4 to x of f(t)dt

Determine the value of each of the following:

g(5)

*print*Print*list*Cite

### 1 Answer

f(x) = 0 when x<-4

f(x) = 3 when -4<=x<-1

f(x) = -4 when -1<=x<4

f(x) = 0 when x>=4

`g(x) = int^x_(-4)f(t) dt`

Since f(x) changes with x we have to break the integral to several parts as x chages.

When `-4lt=xlt-1`

g(x)

`= int^x_(-4)f(t) dt`

`= int^x_(-4)3dt`

`= [3x]^x_(-4)`

`= 3x+12`

When `-1lt=xlt4`

g(x)

`= int^x_(-4)f(t) dt`

`= int^x_(-4)(-4) dt`

`= [-4x]^x_(-4)`

`= -4x-16`

When x>4

g(x)

`= int^x_(-4)f(t) dt`

`= int^x_(-4)(0) dt`

`= 0`

From `-4lt=xlt-1`

**g(x) = 3x+12**

When` -1lt=xlt4`

**g(x) = -4x-16**

When `xgt=4`

**g(x) = 0**

g(5) will occur when x>5 related to x>=4

**g(5) = 0**

**Sources:**