Matematika

Pertanyaan

Tolong caranya gimana ya??
Tolong caranya gimana ya??

1 Jawaban

  • MisalĀ [tex]u = 25-x^{2} \\ \frac{du}{dx}=-2x \\ \frac{du}{-2x}=dx \\[/tex].
    [tex]\int_{3}^{4} 11x\sqrt{25-x^{2}} dx \\ = \int_{3}^{4} 11x (u^{\frac{1}{2}}) \frac{du}{-2x} \\ =-\frac{11}{2}\int_{3}^{4}u^{\frac{1}{2}} du \\ = -\frac{11}{2} [\frac{2}{3}u^{\frac{3}{2}}]_{3}^{4} \\ = -\frac{11}{2}[\frac{2}{3}(25-x^{2})\sqrt{25-x^{2}}]_{3}^{4} \\ = -\frac{11}{2}([\frac{2}{3}\times 9\sqrt{9}]-[\frac{128}{3}]) \\ = -\frac{11}{2}([\frac{54}{3}]-[\frac{128}{3}]) \\ = -\frac{11}{2}(-\frac{74}{3}) \\ = \frac{814}{6} \\ = \frac{407}{3} \\[/tex]