A variant antiderivative problem

Calculus Level 1

Given that $A$ is a real number greater than 1, and that $\displaystyle\int_{1}^{A} \frac {dx}x = 2$ .

Find $A$ to 2 decimal places.

2 solutions

Denton Young
Sep 23, 2019

The antiderivative of $1/x$ is $ln x$

So we need to solve $ln A - ln 1 = 2$

$ln 1 = 0$

So $ln A = 2$

$A = e^2 = 7.39$

Got the answer the same way

A Former Brilliant Member - 1 year, 8 months ago

Chew-Seong Cheong
Sep 24, 2019

$\begin{aligned} \int_1^A \frac {dx}x & = 2 \\ \ln x \ \big|_1^A & = 2 \\ \ln A & = 2 \\ A & = e^2 \approx \boxed{7.39} \end{aligned}$