What is the integral from x-z to x+z of z ?

The integral from x-z to x+z of z is 2xz

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integral from x-z to x+z of z

\int_{x - z}^{x + z} z d z

2 x z

Solution steps

\int_{x - z}^{x + z} z d z

Apply the Power Rule

: [\frac{z ^{2}}{2}]_{x - z}^{x + z}

= [\frac{z ^{2}}{2}]_{x - z}^{x + z}

Compute the boundaries:

\frac{( x + z ) ^{2}}{2} - \frac{( x - z ) ^{2}}{2}

= \frac{( x + z ) ^{2}}{2} - \frac{( x - z ) ^{2}}{2}

Simplify

= 2 x z

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\int_{0}^{3} \frac{1}{x + 1} d x

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What is the integral from x-z to x+z of z ?
The integral from x-z to x+z of z is 2xz