Evaluate integral01 (1)/(sqrt(9x2 - 1)) dx

April 9, 2026Mathematics

ScanSolve AI Answer

April 9, 2026

Answer

\frac{1}{3} $to$ x

Here are the solutions to the integration problems.

: Evaluate $\int_0^1 \frac{1}{\sqrt{9x^2 - 1}} \, dx$

Assumption: The integrand $\frac{1}{\sqrt{9x^2 - 1}}$ is only defined for $9x^2 - 1 > 0$ , which means $x^2 > \frac{1}{9}$ , or $x > \frac{1}{3}$ or $x < -\frac{1}{3}$ . Since the lower limit of integration is $0$ , the integral as written is improper and undefined in real numbers over the interval $[0, 1]$ . We will evaluate the integral from $x = \frac{1}{3}$ to $x

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Quick Answer

Here are the solutions to the integration problems.
Since the lower limit of integration is 0, the integral as written is improper and undefined in real numbers over the interval [0, 1].
We will evaluate the integral from x = (1)/(3) to $x.

Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 9, 2026

Here are the solutions to the integration problems. Problem 1: Evaluate _0^1 (1)/(sqrt(9x^2 - 1)) \, dx Assumption: The integrand (1)/(sqrt(9x^2 - 1)) is only defined for 9x^2 - 1 > 0, which means x^2 > (1)/(9), or x > (1)/(3) or x < -(1)/(3). Since the lower limit of integration is 0, the integral as written is improper and undefined in real numbers over the interval [0, 1]. We will evaluate the integral from x = (1)/(3) to $x