Tích phân \(\int\limits^{\frac{\pi}{2}}_0\left(1-\cos x\right)^n\sin x\text{d}x\) bằng
\(\dfrac{1}{2n}\). \(\dfrac{1}{n+1}\). \(\dfrac{1}{n-1}\). \(\dfrac{1}{2n-1}\). Hướng dẫn giải:\(\int\limits^{\frac{\pi}{2}}_0\left(1-\cos x\right)^n\sin x\text{d}x=\int\limits^{\frac{\pi}{2}}_0\left(1-\cos x\right)^n\text{d}\left(1-\cos x\right)\)
\(=\dfrac{\left(1-\cos x\right)^{n+1}}{n+1}|^{\frac{\pi}{2}}_0\)
\(=\dfrac{1}{n+1}\).