Question

pls bantu ngerjakan caranya, tapi hasil jawabannya harus 1/8, yang diperlukan hanya cara pengerjaannya saja​

Answer 1

Verified answer

[tex]\begin{aligned}\int_1^2\left(\frac{x-1}{x^3}\right)\ dx&=\int_1^2 \frac{x}{x^3}-\frac{1}{x^3}\ dx \\ &=\int_1^2 \frac{1}{x^2}-\frac{1}{x^3}\ dx \\ &=\int_1^2 x^{-2}-x^{-3}\ dx \\ &=\frac{x^{-1}}{-1}-\frac{x^{-2}}{-2}|^2_1 \\ &=-\frac{1}{x}+\frac{1}{2x^2}|^2_1 \\ &=\left(-\frac{1}{2}+\frac{1}{2(2)^2}\right)-\left(-\frac{1}{1}+\frac{1}{2(1)^2}\right) \\ &=\left(-\frac{1}{2}+\frac{1}{8}\right)-\left(-1+\frac{1}{2}\right) \\ &=\frac{1}{8}\end{aligned}[/tex]