Question
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A graph of ff is shown above. The numbers shown represent the geometric area of each region. Evaluate the following definite integrals.

∫0 to 1              f(x)dx

∫0 to 2              f(x)dx

∫0 to 3              f(x)dx

∫1 to 2             -3f(x)dx

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Step 1

As you have asked a question containing multiple subparts and not mentioning which subparts to be solved, so we will be solving the first three subparts for you. If you want the solution of other subparts too then please mention the subparts for which you want to get the solution and upload the question again.

If the curve lies below the x-axis then the modulus of the area under the curve is considered.

If the curve lies above the x-axis then the modulus of the area under the curve is not considered.

Step 2

Now, as per the graph in the interval (0,1), the graph lies below the x-axis so the modulus of the area is considered.

In the interval (1,2), the graph lies above the x-axis so the modulus of the area is not considered.

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