Übung$\int_{\sqrt{y}}^{t^2\sin\left(y\right)}\left(\frac{\sin\left(x\right)}{x}\right)dx$
Schritt-für-Schritt-Lösung
1
Wenden Sie die Formel an: $\int\frac{\sin\left(\theta \right)}{\theta }dx$$=\theta +\frac{-\theta ^3}{18}+\frac{\theta ^5}{600}+\frac{-\theta ^7}{35280}+C$
$\left[\left(x+\frac{-x^3}{18}+\frac{x^5}{600}+\frac{-x^7}{35280}\right)\right]_{\sqrt{y}}^{t^2\sin\left(y\right)}$
2
Wenden Sie die Formel an: $\left[x\right]_{a}^{b}$$=eval\left(x,b\right)-eval\left(x,a\right)+C$, wobei $a=\sqrt{y}$, $b=t^2\sin\left(y\right)$ und $x=x+\frac{-x^3}{18}+\frac{x^5}{600}+\frac{-x^7}{35280}$
$t^2\sin\left(y\right)+\frac{-\left(t^2\sin\left(y\right)\right)^3}{18}+\frac{\left(t^2\sin\left(y\right)\right)^5}{600}+\frac{-\left(t^2\sin\left(y\right)\right)^7}{35280}-\left(\sqrt{y}+\frac{-\left(\sqrt{y}\right)^3}{18}+\frac{\left(\sqrt{y}\right)^5}{600}+\frac{-\left(\sqrt{y}\right)^7}{35280}\right)$
Zwischenschritte
3
Vereinfachen Sie den Ausdruck
$t^2\sin\left(y\right)+\frac{-\left(t^2\sin\left(y\right)\right)^3}{18}+\frac{\left(t^2\sin\left(y\right)\right)^5}{600}+\frac{-\left(t^2\sin\left(y\right)\right)^7}{35280}-\sqrt{y}+\frac{\sqrt{y^{3}}}{18}+\frac{-\sqrt{y^{5}}}{600}+\frac{\sqrt{y^{7}}}{35280}$
Erläutern Sie diesen Schritt näher
Endgültige Antwort auf das Problem $t^2\sin\left(y\right)+\frac{-\left(t^2\sin\left(y\right)\right)^3}{18}+\frac{\left(t^2\sin\left(y\right)\right)^5}{600}+\frac{-\left(t^2\sin\left(y\right)\right)^7}{35280}-\sqrt{y}+\frac{\sqrt{y^{3}}}{18}+\frac{-\sqrt{y^{5}}}{600}+\frac{\sqrt{y^{7}}}{35280}$