What is the integral from 0 to 2.1 of pi(21/10-x)^2 ?

The integral from 0 to 2.1 of pi(21/10-x)^2 is (3087pi)/(1000)

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integral from 0 to 2.1 of pi(21/10-x)^2

\int_{0}^{2.1} π (\frac{21}{10} - x)^{2} d x

\frac{3087 π}{1000}

Decimal Notation

9.69809 \dots

Solution steps

\int_{0}^{2.1} π (\frac{21}{10} - 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}^{2.1} (\frac{21}{10} - x)^{2} d x

Apply u-substitution

: \int_{\frac{21}{10}}^{0} - u^{2} d u

= π \cdot \int_{\frac{21}{10}}^{0} - u^{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= π (- \int_{0}^{\frac{21}{10}} - u^{2} d u)

Take the constant out:

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

= π (- (- \int_{0}^{\frac{21}{10}} u^{2} d u))

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{\frac{21}{10}}

= π (- (- [\frac{u ^{3}}{3}]_{0}^{\frac{21}{10}}))

Simplify

= π [\frac{u ^{3}}{3}]_{0}^{\frac{21}{10}}

Compute the boundaries:

\frac{3087}{1000}

= π \frac{3087}{1000}

Simplify

= \frac{3087 π}{1000}

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What is the integral from 0 to 2.1 of pi(21/10-x)^2 ?
The integral from 0 to 2.1 of pi(21/10-x)^2 is (3087pi)/(1000)