`f(x) = 5x^4 - 2x^5, F(0) = 4` Find the antiderivative `F` that satisfies the given condition. Check your answer by comparing the graphs of `f` and `F`.

Textbook Question

Chapter 4, 4.9 - Problem 23 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the antiderivative F,under the given condition, such that:

`int f(x)dx = F(x) + c`

Hence, you need to evaluate the indefinite integral of function f(x), such that:

`int (5x^4 - 2x^5)dx = 5x^5/5 - 2x^6/6 + c`

`int (5x^4 - 2x^5)dx = x^5 - x^6/3 + c`

The problem provides the information that F(0) = 4, hence, replacing 0 for x in `F(x) = x^5 - x^6/3 + c` yields:

`F(0) = 0^5 - 0^6/3 + c => c = 4`

Hence, evaluating the antiderivative F(x), yields` F(x) = x^5 - x^6/3 + 4.`

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