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Determine the function f ( x ) .
f ′ ( x )= 4x3 - 9 + 2 sin x + 7ex , f (0) = 15
Solution
The first step is to integrate to fine out the most general possible
f ( x ) = ∫ 4x3 - 9 + 2 sin x + 7ex
= x4 - 9 x - 2 cos x + 7ex + c
Now we contain a value of the function therefore let's plug in x = 0 and determine the value of the constant of integration c.
15 = f (0) = 04 - 9 (0) - 2 cos (0) + 7e0 + c
= -2 + 7 + c
= 5 +c
Thus, from this it looks like c = 10 . it means that the function is,
f ( x ) = x4 - 9x - 2 cos x + 7ex + 10
8
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