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

The integral from 0 to 1 of pi(5x)^2 is (25pi)/3

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integral from 0 to 1 of pi(5x)^2

\int_{0}^{1} π (5 x)^{2} d x

\frac{25 π}{3}

Decimal

26.17993 \dots

Solution steps

\int_{0}^{1} π (5 x)^{2} d x

Take the constant out:

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

= π \cdot \int_{0}^{1} (5 x)^{2} d x

Simplify

(5 x)^{2} : 25 x^{2}

= π \cdot \int_{0}^{1} 25 x^{2} d x

Take the constant out:

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

= π 25 \cdot \int_{0}^{1} x^{2} d x

Apply the Power Rule

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

= π 25 [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= π 25 \cdot \frac{1}{3}

Simplify

= \frac{25 π}{3}

\frac{d}{d x} (5 - 5 x^{2})

6 y^{^{''}} - 6 y^{^{'}} + 75 y = 0

y^{^{'}} = \frac{2 x}{1 + 2 y}, y (2) = 0

ln (ln (7 x))

\int \frac{cos ( 6 x )}{sin ( 6 x )} d x

What is the integral from 0 to 1 of pi(5x)^2 ?
The integral from 0 to 1 of pi(5x)^2 is (25pi)/3