Evaluate the integral. (Use C for the constant of integration.) Integral of e^{4 theta} sin(5...


Evaluate the integral. (Use {eq}C{/eq} for the constant of integration.)

{eq}\displaystyle \int e^{4\theta} \:\text{sin}\:(\text{5}\theta) \:d\theta{/eq}

Integration by Parts method:

In mathematics, finding the integration or antiderivative of a function is the inverse process of differentiation. The by parts method of the integration is a special method that comes in the picture when two functions (multiple of two functions) come together in the integrand.

According to the integration by parts method:

{eq}\int {f(t)g(t)} dt = f(t)\int {g(t)dt} - \int {\left( {\dfrac{d}{{dt}}f(t)\int {g(t)dt} } \right)} dt {/eq}

Answer and Explanation: 1

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Given Data:

  • The given integral is: {eq}I = \int {{e^{4\theta }}} \sin \left( {5\theta } \right)d\theta {/eq}.

Apply integration by parts method...

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Learn more about this topic:

Using Integration By Parts


Chapter 13 / Lesson 7

Learn how to use and define integration by parts. Discover the integration by parts rule and formula. Learn when and how to use integration by parts with examples.

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