Übung
$\int_0^{2\pi}\:\:\frac{1}{4}cos^6xdx$
Schritt-für-Schritt-Lösung
Learn how to solve problems step by step online. int(1/4cos(x)^6)dx&0&2pi. Wenden Sie die Formel an: \int_{a}^{b} cxdx=c\int_{a}^{b} xdx, wobei a=0, b=2\pi , c=\frac{1}{4} und x=\cos\left(x\right)^6. Wenden Sie die Formel an: \int\cos\left(\theta \right)^ndx=\frac{\cos\left(\theta \right)^{\left(n-1\right)}\sin\left(\theta \right)}{n}+\frac{n-1}{n}\int\cos\left(\theta \right)^{\left(n-2\right)}dx, wobei n=6. Wenden Sie die Formel an: \int\cos\left(\theta \right)^ndx=\frac{\cos\left(\theta \right)^{\left(n-1\right)}\sin\left(\theta \right)}{n}+\frac{n-1}{n}\int\cos\left(\theta \right)^{\left(n-2\right)}dx, wobei n=4. Wenden Sie die Formel an: x\left(a+b\right)=xa+xb, wobei a=\frac{\cos\left(x\right)^{3}\sin\left(x\right)}{4}, b=\frac{3}{4}\int\cos\left(x\right)^{2}dx, x=\frac{5}{6} und a+b=\frac{\cos\left(x\right)^{3}\sin\left(x\right)}{4}+\frac{3}{4}\int\cos\left(x\right)^{2}dx.
Endgültige Antwort auf das Problem
$0.25\cdot \left(\frac{\cos\left(2\pi \right)^{5}\sin\left(2\pi \right)}{6}+\frac{5\cdot \cos\left(2\pi \right)^{3}\sin\left(2\pi \right)}{24}+0.625\cdot \left(\pi +0.25\sin\left(4\pi \right)\right)\right)$