What is the integral from a to b of 5x^3 ?

The integral from a to b of 5x^3 is (5(b^4-a^4))/4

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integral from a to b of 5x^3

\int_{a}^{b} 5 x^{3} d x

\frac{5 ( b ^{4} - a ^{4} )}{4}

Solution steps

\int_{a}^{b} 5 x^{3} d x

Take the constant out:

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

= 5 \cdot \int_{a}^{b} x^{3} d x

Apply the Power Rule

= 5 [\frac{x ^{4}}{4}]_{a}^{b}

Compute the boundaries:

\frac{b ^{4}}{4} - \frac{a ^{4}}{4}

= 5 (\frac{b ^{4}}{4} - \frac{a ^{4}}{4})

Simplify

= \frac{5 ( b ^{4} - a ^{4} )}{4}

What is the integral from a to b of 5x^3 ?
The integral from a to b of 5x^3 is (5(b^4-a^4))/4