No calculator! Integrate.

1. $\int _ { 0 } ^ { 8 } | x - 4 | d x$

   Hint 1(a):

   You could rewrite the integrand as a piecewise function and then integrate each piece separately, or...

   Hint 2(a):

   You could think about the shape of the graph of $y = \left|y − 4\right|$ and evaluate this integral geometrically.

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

   Hint (b):

   Before integrating, distribute the $w$.

3. $\int _ { - 1 } ^ { - 5 } - 7 d x$

   Hint (c):

   Before integrating, think about the shape of the graph of $y = −7$. Evaluate this integral geometrically. Careful: Will the area be positive or negative?

4. $\int _ { 0 } ^ { 5 } \sqrt { 25 - x ^ { 2 } } d x$

   Hint (d):

   Before integrating, think about the shape of the graph of $y=\sqrt{25-x^{2}}$.

   Evaluate this integral geometrically.