Evaluate the following integrals without a calculator.

1. $\int _ { - 1 } ^ { - 1 } ( - 9 t ^ { 6 / 5 } - 15 t ^ { - 11 / 3 } ) d t$ 

   Hint (a):

   Take the anti-derivative first.

2. $\int _ { 0 } ^ { 2 } \frac { d } { d x } ( 9 x - 1 ) d x$ 

   Hint (b):

   Fundamental Theorem of Calculus, Part 1

3. $\int ( - 32 t + 12 ) d t$ 

   Answer (c):

   $−16t^2 + 12t + C$

4. $\int \operatorname { cos } ( 5 x ) d x$ 

   Hint (d):

   $k \sin(5x) + C$
   Determine $k$.

5. $\int _ { 1 } ^ { - 1 } ( 4 x ^ { 2 } - 6 x ) d x + \int _ { 1 } ^ { 2 } ( 2 x ^ { 2 } - 3 x ) d x$ 

   Answer (e):

   $\frac{4}{3}x^3-3x^2\Big|_1^{-1}-\frac{2}{3}x^3-\frac{3}{2}x^2\Big|_1^2=-\frac{7}{3}$