Evaluate the integral: {eq}\int_{0}^{\frac{\pi}{4}} \ln(2 \sec x) \, \mathrm{d}x {/eq}.


Evaluate the integral: {eq}\int_{0}^{\frac{\pi}{4}} \ln(2 \sec x) \, \mathrm{d}x {/eq}.


Some important rules of integrals are as follows:

1. {eq}\int [f(x)+g(x)]\ dx = \int f(x)\ dx +\int g(x)\ dx {/eq}

2. {eq}\int [f(x)-g(x)]\ dx = \int f(x)\ dx -\int g(x)\ dx {/eq}

3. {eq}\int [f(x) \cdot g(x)]\ dx = f(x)\int g(x) dx- \int \left[\frac{df(x)}{dx}\int g(x)\ dx \right]\ dx {/eq}

Answer and Explanation: 1

Become a member to unlock this answer!

View this answer

Consider two Integrals:

{eq}P=\int_{0}^{\frac{\pi}{4}} \ln(\sec x)dx\\ Q=\int_{0}^{\frac{\pi}{4}} \ln(\csc x)dx {/eq}

Let us find the Sum P+Q and...

See full answer below.

Learn more about this topic:

Definite Integrals: Definition


Chapter 12 / Lesson 6

A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.

Related to this Question

Explore our homework questions and answers library