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Definite integrals of piecewise functions

AP.CALC: FUN‑6 (EU), FUN‑6.B (LO), FUN‑6.C (LO)

Problem

f(x)={2x+6for    x<22cos(πx)for    x2f(x) = \begin{cases} -2x +6 & \text{for} ~~~~x\lt2 \\ 2\cos(\pi x) & \text{for} ~~~~ x \geq2\end{cases}
Evaluate the definite integral.
integral, start subscript, 1, end subscript, start superscript, 4, end superscript, f, left parenthesis, x, right parenthesis, d, x, equals
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