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

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

Before integrating, distribute the $w$.

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

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

Evaluate this integral geometrically.