# Let g(x)=#int_0^xf(t)dt# where #f# is the function whose graph is shown. Evaluate g(0), g(2), g(4), g(6) and g(12)?

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I find that g(0)=0. I think that g(2) should be 4 since the area is 4 squares but its not correct?

I find that g(0)=0. I think that g(2) should be 4 since the area is 4 squares but its not correct?

##### 1 Answer

# g(0) = 0 #

# g(2) = 8 #

# g(4) = 20 #

# g(6) = 28 #

# g(12) = 8 #

#### Explanation:

We have:

# g(x) =int_0^x \ f(t) \ dt #

So that

**Part (1):**

# g(0) = int_0^0 \ f(t) \ dt #

# \ \ \ \ \ \ \= 0 \ \ \ # (By definition)

**Part (2):**

# g(2) = int_0^2 \ f(t) \ dt #

# \ \ \ \ \ \ \= 4 xx 2 \ \ \ # (Area of rectangle)

# \ \ \ \ \ \ \= 8 #

**Part (3):**

# g(4) = int_0^4 \ f(t) \ dt #

# \ \ \ \ \ \ \= g(2) + 1/2(4+8)(2) \ \ \ # ( + trapezium)

# \ \ \ \ \ \ \= 8 +12 #

# \ \ \ \ \ \ \= 20 #

**Part (4):**

# g(6) = int_0^6 \ f(t) \ dt #

# \ \ \ \ \ \ \= g(4) + 1/2(2)(8) \ \ \ # ( +#triangle# )

# \ \ \ \ \ \ \= 20+8 #

# \ \ \ \ \ \ \= 28 #

**Part (5):**

# g(12) = int_0^12 \ f(t) \ dt #

# \ \ \ \ \ \ \= g(6) - 1/2(8+2)(4) \ \ \ # ( + trapezium below)

# \ \ \ \ \ \ \= 28 - (10(2) #

# \ \ \ \ \ \ \= 8 #