Collins Lawson
04/27/2024 · High School
29. \( \int_{0}^{\pi} \tan x d x= \)
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Step-by-step Solution
The integral of \( \tan x \) with respect to \( x \) cannot be directly calculated. However, we can use the property of the integral of \( \tan x \) to find the result.
The integral of \( \tan x \) with respect to \( x \) is \( -\ln|\cos x| + C \), where \( C \) is the constant of integration.
Therefore, the integral \( \int_{0}^{\pi} \tan x dx \) can be calculated as follows:
\[ \int_{0}^{\pi} \tan x dx = -\ln|\cos x| \Big|_{0}^{\pi} \]
\[ = -\ln|\cos(\pi)| - (-\ln|\cos(0)|) \]
\[ = -\ln(-1) - (-\ln(1)) \]
\[ = \ln(1) - \ln(1) \]
\[ = 0 \]
So, \( \int_{0}^{\pi} \tan x dx = 0 \).
Quick Answer
\( \int_{0}^{\pi} \tan x dx = 0 \)
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