What is the integral from 0 to 1 of (3x)^2 ?

The integral from 0 to 1 of (3x)^2 is 3

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integral from 0 to 1 of (3x)^2

\int_{0}^{1} (3 x)^{2} d x

3

Solution steps

\int_{0}^{1} (3 x)^{2} d x

Simplify

(3 x)^{2} : 9 x^{2}

= \int_{0}^{1} 9 x^{2} d x

Take the constant out:

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

= 9 \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

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

= 9 [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= 9 \cdot \frac{1}{3}

Simplify

= 3

\frac{4 s - 18}{s ^{2} - 6 s + 10}

y = x + 5

\frac{d y}{d x} + a y = 0

x \to - 2 lim (3 x^{4} + 2 x^{2} - x + 1)

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3}, y (0) = 1, y^{^{'}} (0) = 0

What is the integral from 0 to 1 of (3x)^2 ?
The integral from 0 to 1 of (3x)^2 is 3