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Activity 4.3.2 .
Use known geometric formulas and the net signed area interpretation of the definite integral to evaluate each of the definite integrals below.
(a)
(b)
\(\int_{-1}^4 (2-2x) \, dx\)
(c)
\(\int_{-1}^1 \sqrt{1-x^2} \, dx\)
(d)
\(\int_{-3}^4 g(x) \, dx\text{,}\) where
\(g\) is the function pictured in the following figure. Assume that each portion of
\(g\) is either part of a line or part of a circle.
