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Class 12 math (India)

Lesson 8: Definite integrals of piecewise functions

Definite integrals of piecewise functions

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

f(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

(Choice A)
start fraction, 1, divided by, 2, end fraction
(Choice B)
3
(Choice C)
start fraction, 1, divided by, 2, end fraction, plus, start fraction, 1, divided by, pi, end fraction
(Choice D)
start fraction, 1, divided by, 2, end fraction, minus, start fraction, 1, divided by, pi, end fraction

Stuck?