en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1/16 of integral from y^{1/4} to 1/2 of cos(16pix^5)

Solution

\int_{0}^{\frac{1}{16}} \int_{y^{\frac{1}{4}}}^{\frac{1}{2}} cos (16 π x^{5}) d x d y

Solution

\frac{1}{80 π}

+1

Decimal Notation

0.00397 \dots

Solution steps

\int_{0}^{\frac{1}{16}} \int_{y^{\frac{1}{4}}}^{\frac{1}{2}} cos (16 π x^{5}) d x d y

Change order of integration

= \int_{0}^{\frac{1}{2}} \int_{0}^{x^{4}} cos (16 π x^{5}) d y d x

\int_{0}^{x^{4}} cos (16 π x^{5}) d y = x^{4} cos (16 π x^{5})

= \int_{0}^{\frac{1}{2}} x^{4} cos (16 π x^{5}) d x

\int_{0}^{\frac{1}{2}} x^{4} cos (16 π x^{5}) d x = \frac{1}{80 π}

= \frac{1}{80 π}

Popular Examples

integral of integral of x^2+y^2

\int \int x^{2} + y^{2} d x d y

integral of integral of x^2y

\int \int x^{2} y d x d y

integral of integral of (x-y)

\int \int (x - y) d x d y

integral of integral of cos(x)

\int \int cos (x) d x d x

integral of integral of x+y

\int \int x + y d x d y

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1/16 of integral from y^{1/4} to 1/2 of cos(16pix^5) ?
The integral from 0 to 1/16 of integral from y^{1/4} to 1/2 of cos(16pix^5) is 1/(80pi)