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Evaluate the definite integral: integral_0^pi/2 cos 2x dx

Question:

Evaluate the definite integral:

{eq}\displaystyle \int_0^{\frac{\pi}{2}} cos\ 2x\ dx {/eq}

Definite Integration:

  • The definite integral of a sine or a cosine function gives the area bounded by the loop of the function in a given interval. We can apply the basic integral formulas to evaluate the integral of these functions and then we need to apply the limits of integration.
  • The following formulas are useful in dealing with definite integrals involving the cosine function:

{eq}\begin{align} & \hspace{1cm} \int_a^b f'(x) dx= f(b)- f(a) \\[0.3cm] &\hspace{1cm}\int \cos (ax) \text{d}x=\frac{\sin (ax) }{a}+C& & \left[\text{ Where }C \text{ is an arbitrary constant of indefinite integration } \right]\\[0.3cm] \end{align} {/eq}

Answer and Explanation: 1

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We have the following given data

{eq}\displaystyle \int_0^{\frac{\pi}{2}} \cos (2x) \ dx= \, ? {/eq}


Solution

{eq}\begin{align} ...

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Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.


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