Evaluate the integral.
{eq}\int_{\pi/4}^{\pi/3} \frac{\ln(\tan x)}{\sin x \cos x} \, \mathrm{d}x {/eq}
Question:
Evaluate the integral.
{eq}\int_{\pi/4}^{\pi/3} \frac{\ln(\tan x)}{\sin x \cos x} \, \mathrm{d}x {/eq}
Integration Using Substitution:
Let's say we have a function {eq}\displaystyle I = \int g(f(x)) \cdot f'(x) dx {/eq}.
If we need to evaluate the value of the integral, we can simplify it first using the method of substitution. For example if {eq}\displaystyle u = f(x) {/eq} then, {eq}\displaystyle du = f'(x) dx {/eq}. Notice that the function {eq}\displaystyle f'(x) dx {/eq} can be replaced by {eq}\displaystyle du {/eq}.
Hence by making these substitutions we get,
{eq}\displaystyle I = \int g(f(x)) f'(x) dx = \int g(u) du {/eq}
Answer and Explanation: 1
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View this answerGiven an integral,
{eq}\displaystyle I = \int_{\pi/3}^{\pi/4} \frac{ \ln \tan x }{ \sin x \cos x } dx {/eq}
We need to evaluate the value of the...
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Chapter 13 / Lesson 13Learn what integration problems are. Discover how to find integration sums and how to solve integral calculus problems using calculus example problems.