Howto solve it the final answer is 5/3 but I do it and I end up 0
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First One:
This is not a smooth function so correspondingly the integration process must be broken up into sections where the function is continuous:
Integral = ∫(1-2x).dx from -1 to ½ + ∫(2x-1).dx from ½ to 1
= (x-x²) from -1 to ½ + (x²-x) from ½ to 1
= [¼+2 ] + [0+½-¼] = 2½ = 5/2. Sorry your 5/3 is wrong!
Second One:
Similarly:
Integral = ∫(-3x).dx from -1 to 0 + ∫x.dx from 1 to 3
Integrate that and put in the limits yourself . The answer is -6.
This is not a smooth function so correspondingly the integration process must be broken up into sections where the function is continuous:
Integral = ∫(1-2x).dx from -1 to ½ + ∫(2x-1).dx from ½ to 1
= (x-x²) from -1 to ½ + (x²-x) from ½ to 1
= [¼+2 ] + [0+½-¼] = 2½ = 5/2. Sorry your 5/3 is wrong!
Second One:
Similarly:
Integral = ∫(-3x).dx from -1 to 0 + ∫x.dx from 1 to 3
Integrate that and put in the limits yourself . The answer is -6.