# Find {eq}f {/eq} given the following information: {eq}f''(x) = 4cos(x), f'(\pi/2) = 0, \; f(0) = 5 {/eq}.

## Question:

Find {eq}f {/eq} given the following information: {eq}f''(x) = 4cos(x), f'(\pi/2) = 0, \; f(0) = 5 {/eq}.

## Indefinite Integration:

Generally, we can define indefinite integration as the reverse process of the derivative of a function. In other words, we can mention this process is an anti-derivative. For example, the result of the integration of the derivative is the function with the constant.

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Given the second derivative is {eq}{f}''(x) = 4 \cos (x) {/eq} and the initial conditions are {eq}{f}'\left( \frac{\pi }{2} \right) = 0 {/eq} and...

Anti-Derivatives: Calculating Indefinite Integrals of Polynomials

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Chapter 13 / Lesson 2
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The fundamental theorem of calculus allows us to calculate indefinite integrals as the anti-derivatives of the original polynomial function. Learn how to calculate indefinite integrals of polynomials through several examples and how to apply a general rule to polynomials with any number of variables.