- #1
hytuoc
- 26
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Some one please show me how to do this problem below
Integral of e^x cos(x) dx
how to I integrate that?
thanks
Integral of e^x cos(x) dx
how to I integrate that?
thanks
The formula for integrating e^x cos(x) is ∫e^x cos(x)dx = 1/2 (e^x (sin(x) + cos(x))) + C.
To solve the integral of e^x cos(x), you can use the integration by parts method, where you choose e^x as the first function and cos(x) as the second function. Then, use the integration by parts formula: ∫u dv = uv - ∫v du. This will reduce the integral to a simpler one that can be easily solved.
Yes, there is an alternative method called the substitution method. In this method, you substitute u = sin(x) and du = cos(x) dx, which will transform the integral into ∫e^x du. This can then be solved by integrating e^x and substituting back the value of u.
Yes, most scientific calculators have a built-in integration function that can solve the integral of e^x cos(x). However, it is important to note that you still need to have a basic understanding of the integration process to properly use the calculator.
Some common mistakes to avoid when integrating e^x cos(x) include forgetting to add the constant of integration, making errors in the substitution or integration by parts process, and forgetting to simplify the final solution. It is also important to check the final answer by differentiating it to ensure its correctness.