What is the integral from 1 to 4 of pi(1/x)^2 ?

The integral from 1 to 4 of pi(1/x)^2 is (3pi)/4

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integral from 1 to 4 of pi(1/x)^2

\int_{1}^{4} π (\frac{1}{x})^{2} d x

\frac{3 π}{4}

Decimal

2.35619 \dots

Solution steps

\int_{1}^{4} π (\frac{1}{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_{1}^{4} (\frac{1}{x})^{2} d x

Simplify

(\frac{1}{x})^{2} : \frac{1}{x ^{2}}

= π \cdot \int_{1}^{4} \frac{1}{x ^{2}} d x

Apply the Power Rule

: [- \frac{1}{x}]_{1}^{4}

= π [- \frac{1}{x}]_{1}^{4}

Compute the boundaries:

\frac{3}{4}

= π \frac{3}{4}

Simplify

= \frac{3 π}{4}

y^{^{'}} = 3 x^{2} y

x \to 0 + lim (\frac{ln ( x )}{csc ( x )})

f (x) = \frac{1}{( 1 - x ) ^{2}}

x \to 0 + lim (2 (tan (x))^{x})

\frac{d y}{d x} = \frac{( x ^{2} + y ^{2} )}{2 x y}

What is the integral from 1 to 4 of pi(1/x)^2 ?
The integral from 1 to 4 of pi(1/x)^2 is (3pi)/4