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Evaluate the integrals and simplify as much as possible.

The value of the integral \( \int_0^1 2^x \, dx \) is \( \frac{1}{\ln(2)} \).

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Here are some related questions for further exploration:

1. What is the antiderivative of \( 2^x \)?
2. How would you solve the integral \( \int 2^{x^2} dx \)?
3. How does the base of the exponential function affect the integration process?
4. Can this result be applied to exponential growth problems?
5. What happens when you change the limits of integration to \( \int_0^b 2^x dx \)?

**Tip:** The logarithmic constant \( \ln(2) \) often appears when integrating functions of the form \( a^x \).

Evaluate the integral \( \int_0^1 2^x \, dx \) and simplify as much as possible.

This page explains how to evaluate the integral \( \int_0^1 2^x \, dx \), simplifying the solution using the properties of exponential functions and natural logarithms. This example helps students learn the application of the fundamental theorem of calculus in definite integrals.

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