Examine the following integrals. Consider the multiple tools available for evaluating integrals and use the best strategy for each part. Evaluate the definite integrals and state the strategies that you used. For the indefinite integrals, find the antiderivative function, if you can.

1. $\int ( 2 y - 3 ) ^ { 2 } d y$

   Hint (a):

   Expand the expression first.

   Answer (a):

   $\frac{4}{3}y^{3}-6y^{2}+9y+C$

2. $\int _ { 1 } ^ { 2 } 2 ^ { 3 x } d x$

   Hint (b):

   Use a calculator.

   Answer (b):

   $≈26.93$, using a calculator.

3. $\int \operatorname { sin } ( x ^ { 2 } ) d x$

4. $\int _ { 0 } ^ { 3 } \sqrt { 9 - x ^ { 2 } } d x$

   Hint (d):

   Do NOT use a calculator.
   What familiar geometric shape is made by the following equation?

   $y=\sqrt{9-x^{2}}$

5. $\int ( 9 m ^ { - 2 } + 7 m ^ { 11 } ) d m$

   Hint (e):

   How can you reverse the Power Rule?