∫ [f(x)+-g(x)] dx
To find the integral of the sum or difference of two functions, f(x) and g(x), we can integrate each function separately and then add or subtract the results
To find the integral of the sum or difference of two functions, f(x) and g(x), we can integrate each function separately and then add or subtract the results. Let’s break down the integral:
∫ [f(x) +- g(x)] dx
First, integrate f(x) with respect to x:
∫ f(x) dx
Next, integrate g(x) with respect to x:
∫ g(x) dx
Finally, add or subtract the two results based on whether the symbol between f(x) and g(x) is “+” or “-“.
If the symbol is “+”, the integral becomes:
∫ [f(x) + g(x)] dx = ∫ f(x) dx + ∫ g(x) dx
If the symbol is “-“, the integral becomes:
∫ [f(x) – g(x)] dx = ∫ f(x) dx – ∫ g(x) dx
So, the integral of the sum or difference of two functions is obtained by integrating each function separately and then adding or subtracting the results based on the symbol between the functions.
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