What is the integral of (x/2)^2 ?

The integral of (x/2)^2 is (x^3)/4-(x^3)/6+C

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integral of (x/2)^2

\int (\frac{x}{2})^{2} d x

\frac{x ^{3}}{4} - \frac{x ^{3}}{6} + C

Solution steps

\int (\frac{x}{2})^{2} d x

Apply Integration By Parts

: \frac{x ^{3}}{4} - \int \frac{x ^{2}}{2} d x

= \frac{x ^{3}}{4} - \int \frac{x ^{2}}{2} d x

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

= \frac{x ^{3}}{4} - \frac{x ^{3}}{6}

Add a constant to the solution

= \frac{x ^{3}}{4} - \frac{x ^{3}}{6} + C

x \to 0 - lim (F (x))

f (x) = 1 + 4 - x, at x = - 2

\int \frac{4 x y - 2 x ^{2}}{2 x ^{3} - x ^{2} y} d y

\int 90 (2 x - 5)^{8} d x

n = 5 \sum \infty 4 - \frac{4}{n ^{2}}