Mathematics

$\displaystyle\int\limits_{a}^{b}f(x)\ dx=b^3-a^3$, then find $f(x)$.

SOLUTION
Given,
$\displaystyle\int\limits_{a}^{b}f(x)\ dx=b^3-a^3$.
Let, $f(x)=3x^2$
Then,
$\displaystyle\int\limits_{a}^{b}f(x)\ dx$
$=\displaystyle\int\limits_{a}^{b}3x^2\ dx$
$=3\left[\dfrac{x^3}3{}\right]_{x=a}^{x=b}$
$=(b^3-a^3)$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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