Question

1. -/1.76 points evaluate the integral. (int_{1}^{49} \frac{1}{2x} dx)

Explanation:

Step1: Use integral rule

The integral of $\frac{1}{x}$ is $\ln|x|$. So, $\int_{1}^{49}\frac{1}{2x}dx=\frac{1}{2}\int_{1}^{49}\frac{1}{x}dx$.

Step2: Evaluate definite - integral

$\frac{1}{2}[\ln|x|]_{1}^{49}=\frac{1}{2}(\ln(49)-\ln(1))$.

Step3: Simplify result

Since $\ln(1) = 0$ and $\ln(49)=\ln(7^{2}) = 2\ln(7)$, we have $\frac{1}{2}(2\ln(7))=\ln(7)$.

Answer:

$\ln(7)$