What is the integral from 0 to 1 of 5x^2 ?

The integral from 0 to 1 of 5x^2 is 5/3

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integral from 0 to 1 of 5x^2

\int_{0}^{1} 5 x^{2} d x

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

\int_{0}^{1} 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

= 5 [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= 5 \cdot \frac{1}{3}

Simplify

= \frac{5}{3}

l a pl a ce t r an s f or m 31

t an g e n t y = 3 x^{3} - x^{2} + 3, (2, 23)

in v erse l a pl a ce \frac{k}{( s - 4 ) ^{3}}

\frac{d}{d x} (sin^{2} (3 x^{2} - 1))

l a pl a ce t r an s f or m t e^{- 2 t} cos (3 t)

What is the integral from 0 to 1 of 5x^2 ?
The integral from 0 to 1 of 5x^2 is 5/3