Find {eq}f {/eq}.

{eq}f'(x) = 1 + 3 \sqrt{x}; f(4) = 25 {/eq}


Find {eq}f {/eq}.

{eq}f'(x) = 1 + 3 \sqrt{x}; f(4) = 25 {/eq}

Finding Function Using Integration:

When the derivative of a function is given and the derivative is only the function of {eq}x {/eq}, then the function will be calculated by integrating the derivative with respect to {eq}x {/eq}. We get a constant after integration and will be calculated on the basis of initial conditions.

Answer and Explanation: 1

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Consider {eq}f'(x) = 1 + 3 \sqrt{x}\,\,\cdots(1) {/eq} and {eq}f(4) = 25 {/eq}.

Integrate the equation (1) with respect to {eq}x {/eq}.


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Indefinite Integrals as Anti Derivatives


Chapter 12 / Lesson 11

Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.

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