What is the integral from c to x of g(x) ?

The integral from c to x of g(x) is (g(x^2-c^2))/2

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integral from c to x of g(x)

\int_{c}^{x} g (x) d x

\frac{g ( x ^{2} - c ^{2} )}{2}

Solution steps

\int_{c}^{x} gx d x

Take the constant out:

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

= g \cdot \int_{c}^{x} x d x

Apply the Power Rule

= g [\frac{x ^{2}}{2}]_{c}^{x}

Compute the boundaries:

\frac{x ^{2}}{2} - \frac{c ^{2}}{2}

= g (\frac{x ^{2}}{2} - \frac{c ^{2}}{2})

Simplify

= \frac{g ( x ^{2} - c ^{2} )}{2}

What is the integral from c to x of g(x) ?
The integral from c to x of g(x) is (g(x^2-c^2))/2