What is the integral from 0 to 1 of xy ?

The integral from 0 to 1 of xy is y/2

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integral from 0 to 1 of xy

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

\frac{y}{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2}

= y \frac{1}{2}

Simplify

= \frac{y}{2}

\frac{d}{d x} ((2 x^{2} + 5) (4 x - 1))

y^{^{''}} - (\frac{3}{x}) y^{^{'}} - (\frac{6}{x ^{2}}) y = 0

ln (5 + e^{x y}) = y

\frac{\partial}{\partial x} (ln (2 x + 2 c t))

\int \frac{9 ( csc ( t ) ) ^{2}}{cot ( t )} d t