What is the integral from 0 to 1/x of xy ?

The integral from 0 to 1/x of xy is 1/(2x)

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integral from 0 to 1/x of xy

\int_{0}^{\frac{1}{x}} x y d y

\frac{1}{2 x}

Solution steps

\int_{0}^{\frac{1}{x}} x y d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int_{0}^{\frac{1}{x}} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{0}^{\frac{1}{x}}

= x [\frac{y ^{2}}{2}]_{0}^{\frac{1}{x}}

Compute the boundaries:

\frac{1}{2 x ^{2}}

= x \frac{1}{2 x ^{2}}

Simplify

= \frac{1}{2 x}

\int_{0}^{- 3} - x^{2} - 3 x d x

\int_{- 1}^{4} (4 x - 3) (x - 3) d x

\int_{0}^{5} (25 - x^{2})^{\frac{1}{2}} d x

\int_{- 1}^{0} (2 + 1 - x^{2}) d x

\int_{0}^{4} (2 + x) d x

What is the integral from 0 to 1/x of xy ?
The integral from 0 to 1/x of xy is 1/(2x)