The largest value among the values of thefunction
i) If a=b then ∆x=0, therefore ∫aaf(x) dx=0
ii) If a<b then ∆x=b-an then a-bn=-∆x
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
The largest value among all the values is F(2)