Exercise · ZW-INDEFINITE-INTEGRAL-011 · ★★★ Advanced
Compute \(\displaystyle\int \sin x\,\cos^{2}x\,dx\).
Choose one option.
Show answer
- B. \(-\frac{\cos^{3} x}{3} + C\)
Explanation
With \(u=\cos x\), \(du=-\sin x\,dx\), the integral is \(-\int u^{2}\,du=-\frac{u^{3}}{3}+C\). Substituting back gives \(-\frac{\cos^{3}x}{3}+C\).
Review the concept: Indefinite integral
The indefinite integral of \(f\) is the family of all its antiderivatives, written with a constant of integration \(C\).
\[\int x^{n}\,dx=\frac{x^{n+1}}{n+1}+C\quad(n\neq-1)\]
More practice problems: indefinite integral
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- ZW-INDEFINITE-INTEGRAL-005 What is ∫ cos x dx?
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- ZW-INDEFINITE-INTEGRAL-008 Compute ∫ (x^2+1)/(x) dx for x>0.