By writing out the sums, determine whether the followingare valid identities.(a)
Chapter 5, Problem 65(choose chapter or problem)
By writing out the sums, determine whether the following are valid identities.
(a) \(\int\left[\sum_{i=1}^{n} f_{i}(x)\right] d x=\sum_{i=1}^{n}\left[\int f_{i}(x) d x\right]\)
(b) \(\int \frac{d}{d x}\left[\sum_{i=1}^{n} f_{i}(x)\right]=\sum_{i=1}^{n}\left[\frac{d}{d x}\left[f_{i}(x)\right]\right]\)
Equation Transcription:
∫∫
∫
Text Transcription:
integral [sum_i=1 ^n f_i (x)] dx= sum_i=1 ^n [integral f_i (x) dx]
integral d/dx [sum_i=1 ^n f_i (x)] = sum_i=1 ^n [d/dx [f_i (x)]]
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