Double Integration - Multivariable Calculus

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Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

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$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Tap to see back →

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx=\int_${0}^{1}$\Big(\int_${x}^{x^2}$ $xy^2$ dy\Big)dx$

Lets deal with the inner integral first.

$\int_${x}^{x^2}$$xy^2$ dy$

$\int_${x}^{x^2}$$xy^2$ $dy=\frac{1}{3}$y^3x$\Big|_${x}^{x^2}$$

Now we evaluate this expression in the outer integral.

$\int_${0}^{1}$ $$\frac{1}{3}$x^7$$-$\frac{1}{3}$x^4dx$$

$=\frac{1}{3}$\int_${0}^{1}$ $x^7$$-x^4dx$$

$=\frac{1}{3}$\Big( $$\frac{1}{8}$x^8$$-$\frac{1}{5}$x^5$\Big)\Big|_${0}^{1}$$

$=\frac{1}{3}$\Big($\frac{1}{8}$-$\frac{1}{5}$\Big)-$\frac{1}{3}$\Big(0-0\Big)$

$=\frac{1}{3}$\Big($\frac{5}{40}$-$\frac{8}{40}$\Big)$

$=\frac{1}{3}$\Big(-$\frac{3}{40}$\Big)=-$\frac{3}{120}$$

Double Integration - Multivariable Calculus

Calculate the following Integral.

Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

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Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

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Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

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Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

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Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

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Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

Calculate the following Integral.

Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

Calculate the following Integral.

Lets deal with the inner integral first. Now we evaluate this expression in the outer integral.

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$

Calculate the following Integral.

$\int_${0}^{1}$\int_${x}^{x^2}$ $xy^2$ dydx$