First slide

Introduction to integration

Question

$If \frac{d}{d x} (f (x)) = 4 x^{3} - \frac{3}{x^{4}} . Such that f (2) = 0 then f (x) is$

Moderate

A

$x^{4} + \frac{1}{x^{3}} - \frac{129}{8}$
B

$x^{3} + \frac{1}{x^{4}} + \frac{129}{8}$
C

$x^{4} + \frac{1}{x^{3}} + \frac{129}{8}$
D

$x^{3} + \frac{1}{x^{4}} - \frac{129}{8}$

Solution

$\begin{array}{l} f (x) = \int (4 x^{3} - \frac{3}{x^{4}}) d x \\ = x^{4} + \frac{1}{x^{3}} + C \\ f (2) = 0 \Rightarrow C = \frac{- 129}{8} \end{array}$

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