Question

The value of integral $\int |2x-8|dx$ will be

• A. $x^2-8x+C$ for $x\in [3,5]$
• B. $8x-x^2+C$ for $x\in [3,5]$
• C. $x^2-8x+C$ for $x\in [4,5]$
• D. $8x-x^2+C$ for $x\in [3,4]$

Answer 1

Answer: (C), (D)

The correct options are
C $x^2-8x+C$ for $x\in [4,5]$
D $8x-x^2+C$ for $x\in [3,4]$

$|2x-8|=2x-8$ for $x>4$ and it is equal to $8-2x$ for $x<4$

First consider $x\le 4$

We have $\int |2x-8|dx=\int (8-2x)dx=8x-x^2+C$

Now consider $x\ge 4$

We have $\int |2x-8|dx=\int (2x-8)dx=x^2-8x+C$

Therefore options $C$ and $D$ are correct