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Popular >

integral from 0 to 1 of integral from 0 to 2 of xye^{xy^2}

Solution

\int_{0}^{1} \int_{0}^{2} x y e^{x y^{2}} d x d y

Solution

\frac{e ^{2} - 1}{2} - 1

+1

Decimal Notation

2.19452 \dots

Solution steps

\int_{0}^{1} \int_{0}^{2} x y e^{x y^{2}} d x d y

\int_{0}^{2} x y e^{x y^{2}} d x = \frac{2 y ^{2} e ^{2 y^{2}} - e ^{2 y^{2}} + 1}{y ^{3}}

= \int_{0}^{1} (\frac{2 y ^{2} e ^{2 y^{2}} - e ^{2 y^{2}} + 1}{y ^{3}}) d y

\int_{0}^{1} (\frac{2 y ^{2} e ^{2 y^{2}} - e ^{2 y^{2}} + 1}{y ^{3}}) d y = \frac{e ^{2} - 1}{2} - 1

= \frac{e ^{2} - 1}{2} - 1

Popular Examples

integral of (e^{2x}+4)^{-1}

\int (e^{2 x} + 4)^{- 1} d x

integral from ln(4) to ln(25) of e^{x/2}

\int_{l n (4)}^{l n (25)} e^{\frac{x}{2}} d x

limit as x approaches 0 of-5/(1-5x)

x \to 0 lim (- \frac{5}{1 - 5 x})

(dy)/(dx)= 1/(sqrt(1-x)),y(0)=1

\frac{d y}{d x} = \frac{1}{1 - x}, y (0) = 1

derivative of f(x)=(x^2+2x-4)/((x+1)^2)derivative of

f (x) = \frac{x ^{2} + 2 x - 4}{( x + 1 ) ^{2}}

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of integral from 0 to 2 of xye^{xy^2} ?
The integral from 0 to 1 of integral from 0 to 2 of xye^{xy^2} is (e^2-1)/2-1