Step 1:

The integral expression is .

Using theorem :

If is integrable on , then .

Where .

The integral expression is .

Here  and .

Substitute in .

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Step 2:

                                ( Since )

Sum of first natural numbers is .

Sum of the squares of first natural numbers is .

Sum of the cubes of first natural numbers is .

Simplify the expression.

.

Solution :

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