Question

How to integrate modulus function??? ​

Answer 1

Answer:

Declare a variable u and substitute it into the integral:

Differentiate u = 4x + 1 and isolate the x term. This gives you the differential, du = 4dx.

Substitute du/4 for dx in the integral:

Evaluate the integral:

Substitute back 4x + 1 for u:

Answer 2

Answer:

Hello....

Step-by-step explanation:

We know that from 0≤x≤1 , the graph is below the x axis and from 1≤x≤2 the graph is above the x axis.

So we can just calculate the integral for both parts and add the positive values of the integrals together instead of calculating the integral from 0 to 2

This will leave us with:

∫02|x2−1|dx=|∫01(x2−1)dx|+|∫12(x2−1)dx|

Hence the answer required is 2/3+4/3=2

So we followed these steps:

1)Choose u and v.

2)Differentiate u: u'

3)Integrate v: ∫v dx.

4)Put u, u' and ∫v dx into: u∫v dx −∫u' (∫v dx) dx.

5)Simplify and solve.