Find the area between the curve $y=\frac{1}{x^{7 / 6}}$ and the $x$-axis from $x=1$ to $\infty$.
square units
Answer
Final Answer: The area between the curve \(y=\frac{1}{x^{7 / 6}}\) and the \(x\)-axis from \(x=1\) to \(\infty\) is \(\boxed{6}\) square units.
Step 1 ：The area under a curve from a point a to b is given by the definite integral of the function from a to b. In this case, we need to find the area under the curve \(y=\frac{1}{x^{7 / 6}}\) from \(x=1\) to \(\infty\). This is equivalent to finding the definite integral of \(\frac{1}{x^{7 / 6}}\) from 1 to \(\infty\).
Step 2 ：The definite integral of \(\frac{1}{x^{7 / 6}}\) from 1 to \(\infty\) is calculated to be 6.
Step 3 ：Final Answer: The area between the curve \(y=\frac{1}{x^{7 / 6}}\) and the \(x\)-axis from \(x=1\) to \(\infty\) is \(\boxed{6}\) square units.
