Apentix/AP Calculus AB/Unit 6: Integration and Accumulation of Change/Question
AP Calculus ABmediummcq1 pt

Which of the following equals ∫(2sin⁡x−cos⁡x) dx\int (2\sin x-\cos x)\,dx?

A.−2cos⁡x−sin⁡x+C-2\cos x-\sin x+C
B.2cos⁡x−sin⁡x+C2\cos x-\sin x+C
C.−2cos⁡x+sin⁡x+C-2\cos x+\sin x+C
D.2cos⁡x+sin⁡x+C2\cos x+\sin x+C

Explanation

Core Concept

The antiderivative of sin⁡x\sin x is −cos⁡x-\cos x and of cos⁡x\cos x is sin⁡x\sin x, so the result is −2cos⁡x−sin⁡x+C-2\cos x-\sin x+C.

Correct Answer

A−2cos⁡x−sin⁡x+C-2\cos x-\sin x+C

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