Evaluate:
{eq}\displaystyle \int_{\displaystyle 0}^{\frac{\displaystyle \pi}{\displaystyle 2}} \; tan(\frac{\displaystyle x}{\displaystyle 2}) dx {/eq}
Question:
Evaluate:
{eq}\displaystyle \int_{\displaystyle 0}^{\frac{\displaystyle \pi}{\displaystyle 2}} \; tan(\frac{\displaystyle x}{\displaystyle 2}) dx {/eq}
Integration in Calculus:
The definite integral is used to calculate the exact area. We are given a tangent trigonometric function.
To solve this problem, we'll use the trig-ratio {eq}\displaystyle \tan(\frac{\displaystyle x}{\displaystyle 2}) = \dfrac{ \sin(\frac{\displaystyle x}{\displaystyle 2}) }{ \cos(\frac{\displaystyle x}{\displaystyle 2}) } {/eq}
Next, we'll apply u-substitution and the common integral {eq}\displaystyle \int u^n \, \mathrm{d}u=\dfrac{u^{n+1}}{n+1}+C. {/eq}.
Answer and Explanation: 1
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View this answerWe are given:
{eq}\displaystyle \int_{\displaystyle 0}^{\frac{\displaystyle \pi}{\displaystyle 2}} \; tan(\frac{\displaystyle x}{\displaystyle 2})...
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Chapter 12 / Lesson 6A 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.