Prove that the function F (x) = e ^ 3x + cosx + x is the antiderivative of the function f (x) = 3e ^ 3x-sinx + 1.
| September 12, 2021 | education
Explanation: To prove that a function is the antiderivative of another function, let’s find its derivative. If the derivative and the second function are equal, then the statement is true.
Solution:
F ‘(x) = (e ^ 3x + cosx + x)’ = (e ^ 3x) ‘+ (cosx)’ + x ‘= (3x)’ * e ^ 3x – sinx + 1 = 3e ^ 3x – sinx + 1;
F ‘(x) = f (x) => the function F (x) = e ^ 3x + cosx + x is the antiderivative f (x) = 3e ^ 3x – sinx + 1.
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