What is the value of this integral #∫_0 ^10 |x−5|dx# ?
1 Answer
Dec 2, 2017
The value of the above integral is 25. It can be solved as follows:
Explanation:
Since we are integrating a modulus function here, we first look for its breaking point, that is the value of x, before and after which the value of |x-5| changes. Also one should keep in mind that modulus always gives positive values, while solving such questions.
- We know that (x-5) <0 for x<5.
#implies # for x#in# [0,5] ; |x-5| = -(x-5) - Also, for X>= 5, (x-5) >0.
#implies# for x ranging from [5,10]; |x-5| = x-5 only as it is positive in this interval.
Now we break our integral into two parts: