Vault Of Euclid

Integrating a Piecewise Function with Sine and a Polynomial

The definite integral warmup

If \[ f(x) = \begin{cases} \sin x & \text{for } x < 0 \\ 3x^{2} & \text{for } x \geq 0 \end{cases} \] find \( \int_{-\pi/2}^{\pi/2} f(x) \, dx \).
calculus-idefinite-integralpiecewise-functionintegrationtrigonometric-functionspolynomial-functionsfundamental-theorem-of-calculusadditivity-of-integralsevaluate-integralsinecosine

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What this problem tests

Tests the student's ability to apply the additivity property of definite integrals and evaluate basic trigonometric and polynomial integrals.

This is a standard Calculus I problem introducing the integration of piecewise functions.

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