Apentix/AP Calculus AB/Unit 6: Integration and Accumulation of Change/Question
AP Calculus ABhardmcq1 pt

Which of the following equals lim⁡n→∞∑i=1n2nsin⁡(3+2in)\lim_{n\to\infty}\sum_{i=1}^{n}\frac{2}{n}\sin\left(3+\frac{2i}{n}\right)?

A.cos⁡5−cos⁡3\cos 5-\cos 3
B.cos⁡3−cos⁡5\cos 3-\cos 5
C.sin⁡5−sin⁡3\sin 5-\sin 3
D.sin⁡3−sin⁡5\sin 3-\sin 5

Explanation

Core Concept

The limit is ∫35sin⁡x dx=[−cos⁡x]35=−cos⁡5+cos⁡3=cos⁡3−cos⁡5\int_3^5\sin x\,dx=[-\cos x]_3^5=-\cos 5+\cos 3=\cos 3-\cos 5.

Correct Answer

Bcos⁡3−cos⁡5\cos 3-\cos 5

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