Question

\(\displaystyle \int (4\cos x-5\sin x)\,dx=\ \ ?\)

• A. \(k+4\sin x+5\cos x\)
• B. \(k-4\sin x-5\cos x\)
• C. \(k+4\sin x-5\cos x\)
• D. \(k-4\sin x+5\cos x\)

Hint:

Linearity: integrate each term, then add a single constant $k$.

Answer 1

The Correct Option is A

Integrate term by term: \(\int 4\cos x\,dx=4\sin x\). \(\int -5\sin x\,dx=5\cos x\). Add the constant \(k\).