What is the integral from 0 to 2 of xy ?

The integral from 0 to 2 of xy is x*2

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integral from 0 to 2 of xy

\int_{0}^{2} x y d y

x \cdot 2

Solution steps

\int_{0}^{2} 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}^{2} y d y

Apply the Power Rule

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

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

Compute the boundaries:

2

= x \cdot 2

\int_{- 1}^{1} \frac{e ^{x}}{1 + e ^{x}} d x

\int_{0}^{6} (x^{2} + x) d x

\int_{- 1}^{1} \frac{1}{4 - x ^{2}} d x

\int_{0}^{1} 2 x d x

\int_{0}^{2} \frac{x}{x ^{2} + 1} d x