1.(a)

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Step 1:

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The integrals are $\"\"$ and $\"\"$ .

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The integral is $\"\"$ .

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Apply Additive interval property $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Solution:

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$\"\"$ .

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1.(b)

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Step 1:

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The integrals are $\"\"$ and $\"\"$ .

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The integral is $\"\"$ .

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Apply Additive interval property $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Solution:

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$\"\"$ .

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1.(c)

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Step 1:

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The integrals are $\"\"$ and $\"\"$ .

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The integral is $\"\"$ .

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Find $\"\"$

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Apply Additive interval property $\"\"$ .

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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Find

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Apply special definition of integrals: $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Solution:

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$\"\"$ .

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1.(d)

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The integral is $\"\"$ .

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Area $\"\"$

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Apply properties of definite integrals: $\"\"$ .

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$\"\"$ \ \

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$\"\"$

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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Back substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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Solution:

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Area is $\"\"$ square-units.

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