What is the integral from 0 to 4 of 6x ?

The integral from 0 to 4 of 6x is 48

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integral from 0 to 4 of 6x

\int_{0}^{4} 6 x d x

48

Solution steps

\int_{0}^{4} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{0}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{4}

= 6 [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= 6 \cdot 8

Simplify

= 48

f (x) = x^{\frac{1}{2}}, (25, 5)

\frac{d}{d x} (f (4 x^{5})) = 8 x^{4}

cos (6 t)

\frac{( 2 x + 7 )}{x}