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3 years ago

Last 2 tutor find it wrong pls help me

Mathematics

1 answer:

Mrac [35]3 years ago

4 0

Answer:

g(x) = 4x² -x +64

Step-by-step explanation:

The integral of f(x) will be continuous. This means the value must be the same for x = 4- as for x = 4+.

For some constant c1, the integral in the region x ≤ 4 is ...

∫f(x)dx = (4x² -x +c1) +C = g(x) +C

The integral in the region x ≥ 4 is given as ...

∫f(x)dx = 31x +C

Evaluated at x=4, we must get the same value from either expression:

4(4²) -4 +c1 +C = 31(4) +C

60 +c1 = 124

c1 = 64

In order to make the integral continuous at x=4, we must have ...

g(x) = 4x² -x +64

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