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 Rewrite the following integral expressions as a single integral.  

  1. Notice that the bounds are the same but the integrands are different. What this means is that, on the interval through , we are subtracting the area under from the area under .

  2. Since both integrands are the same, , notice the bounds. The first integral has bounds that move forward, starting at and
    ending at . While the second integral has bounds that move backwards, from to . What area remains?

  3. Refer to the hint in part (a). Remember that you can factor out .

  4. Notice that both the integrands and the bounds are different. The only thing that these integrals have in common is the distance between the bounds: . We can shift the first integral units to the right to match the second integral, or vice versa.

    You will not change the bounds, be sure to shift the function accordingly:
    will shift the function units to the right.
    will shift the function units to the left.