Question

Determine l=
∫4x2dx
,given that l= 25when l=25 when x=3.

Answer 1

Answer on Question #45742 – Math – Integral Calculus

Question.

Determine $I = \int 4x^{2}dx$, given that $I = 25$ when $x = 3$.

Solution.

$$I = \int 4x^{2}dx = \frac{4}{3}x^{3} + c. \text{ Let } x = 3. \text{ Then } I = \frac{4}{3}3^{3} + c = 36 + c = 25 \Rightarrow c = -11. \text{ So }$$ $$I = \frac{4}{3}x^{3} - 11.$$

Answer. $I = \frac{4}{3}x^{3} - 11$.

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