#### To determine

**To find:**

The largest value among the values of thefunction

#### Answer

F(2)

#### Explanation

**1) Concept:**

i) If a=b then ∆x=0, therefore ∫aaf(x) dx=0

ii) If a<b then ∆x=b-an then a-bn=-∆x

Therefore,

∫abfxdx=-∫bafxdx

**2) Given:**

Fx=∫2xftdt

**3) Calculation:**

The given figures depict the area of a function between the curve and x axis

First, calculate the area for different intervals of a function.

**A) **For F(0) put x=0 in the given integral. Thus ∫20f0dx=-∫02f0dx=- Area of the shaded region. This is negative, therefore,F(0) should lie below x-axis.

**B) **For F(1) put x=1 in thegiven integral ∫21f1dx=-∫12f1dx=- Area of the shaded region. This is negative, therefore,F(1) should lie below x-axis.

**C) **For F(2) put x=2 in thegiven integral ∫22f2dx=0

**D) **For F(3) put x=3 in thegiven integral ∫23f1dx= Area of the shaded region. The region lies below x-axis therefore,F(3) should be negative

**E) **For F(4) put x=4 in thegiven integral ∫24f1dx= Area of shaded region. The region lies below x-axis, therefore,F(4) should be negative

Hence, of the quantities A to E all areas are negative except C, which is 0, and therefore, it is the largest among all the values

**Conclusion:**

The largest value among all the values is F(2)