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Popular Calculus >

integral from 1 to 32 of (sin(\sqrt[5]{x}))/(\sqrt[5]{x^4)}

Solution

\int_{1}^{32} \frac{sin ( 5 x )}{5 x ^{4}} d x

Solution

5 (- cos (2) + cos (1))

+1

Decimal

4.78224 \dots

Solution steps

\int_{1}^{32} \frac{sin ( 5 x )}{5 x ^{4}} d x

Apply u-substitution

= \int_{1}^{2} 5 sin (u) d u

Take the constant out:

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

= 5 \cdot \int_{1}^{2} sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= 5 [- cos (u)]_{1}^{2}

Compute the boundaries:

- cos (2) + cos (1)

= 5 (- cos (2) + cos (1))

Graph

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x \to 0 lim (\frac{( 1 )}{x ^{2}})

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\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 6 x} d x

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x \to - 6 lim (x + 1)

integral of 1/(y^2sqrt(5-y^2))

\int \frac{1}{y ^{2} 5 - y ^{2}} d y

Frequently Asked Questions (FAQ)

What is the integral from 1 to 32 of (sin(\sqrt[5]{x}))/(\sqrt[5]{x^4)} ?
The integral from 1 to 32 of (sin(\sqrt[5]{x}))/(\sqrt[5]{x^4)} is 5(-cos(2)+cos(1))