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 = |y − 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?

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

Evaluate this integral geometrically.