O valor da Integral \int _1^3\int _0^{y^1}\int _{-1}^1dvdy
a. -5
b. 1
c. 5
d. 2
e. 0
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Solução!
![\displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1} \displaystyle\int _{-1}^{1}ydv\\\\\\\ \displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1} \displaystyle\int _{-1}^{1}ydzdydx\\\\\\\ \displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}ydxdy\bigg[z\bigg]_{-1} ^{1}\\\\\\\\\ \displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}ydxdy\bigg[1-(-1)\bigg]\\\\\\\
\displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}ydxdy\bigg[2\bigg]\\\\\\\
\displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}2ydxdy](https://tex.z-dn.net/?f=+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B1%7D+%5Cdisplaystyle%5Cint+_%7B-1%7D%5E%7B1%7Dydv%5C%5C%5C%5C%5C%5C%5C+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B1%7D+%5Cdisplaystyle%5Cint+_%7B-1%7D%5E%7B1%7Dydzdydx%5C%5C%5C%5C%5C%5C%5C+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B1%7Dydxdy%5Cbigg%5Bz%5Cbigg%5D_%7B-1%7D+%5E%7B1%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B1%7Dydxdy%5Cbigg%5B1-%28-1%29%5Cbigg%5D%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B1%7Dydxdy%5Cbigg%5B2%5Cbigg%5D%5C%5C%5C%5C%5C%5C%5C+%0A%0A%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D%5Cdisplaystyle%5Cint_%7B0%7D%5E%7B1%7D2ydxdy%0A%0A+ "\displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1} \displaystyle\int _{-1}^{1}ydv\\\\\\\ \displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1} \displaystyle\int _{-1}^{1}ydzdydx\\\\\\\ \displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}ydxdy\bigg[z\bigg]_{-1} ^{1}\\\\\\\\\ \displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}ydxdy\bigg[1-(-1)\bigg]\\\\\\\
\displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}ydxdy\bigg[2\bigg]\\\\\\\
\displaystyle\int_{1}^{3}\displaystyle\int_{0}^{1}2ydxdy")
![\displaystyle\int_{1}^{3}dx\bigg[2y\bigg]_{0} ^{1} \\\\\\\
2\displaystyle\int_{1}^{3}dx\bigg[ \frac{y^{2} }{2} \bigg]_{0} ^{1} \\\\\\\
2. \dfrac{1}{2}~~ \displaystyle\int_{1}^{3}dx\bigg[ y^{2} \bigg]_{0} ^{1} \\\\\\\
2. \dfrac{1}{2}~~ \displaystyle\int_{1}^{3}dx\bigg[ 1^{2} -0^{2} \bigg] \\\\\\\
2. \dfrac{1}{2}~~ \displaystyle\int_{1}^{3}1.dx\\\\\\\
2. \dfrac{1}{2}~~ \bigg[x\bigg]_{1}^{3}\\\\\\\
2. \dfrac{1}{2}~~ \bigg[3-1\bigg]\\\\\\\
2. \dfrac{1}{2}~~ \bigg[2\bigg]\\\\\\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7Ddx%5Cbigg%5B2y%5Cbigg%5D_%7B0%7D+%5E%7B1%7D+%5C%5C%5C%5C%5C%5C%5C%0A2%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7Ddx%5Cbigg%5B+%5Cfrac%7By%5E%7B2%7D+%7D%7B2%7D+%5Cbigg%5D_%7B0%7D+%5E%7B1%7D+%5C%5C%5C%5C%5C%5C%5C%0A2.+%5Cdfrac%7B1%7D%7B2%7D%7E%7E+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7Ddx%5Cbigg%5B+y%5E%7B2%7D+%5Cbigg%5D_%7B0%7D+%5E%7B1%7D+%5C%5C%5C%5C%5C%5C%5C%0A2.+%5Cdfrac%7B1%7D%7B2%7D%7E%7E+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7Ddx%5Cbigg%5B+1%5E%7B2%7D+-0%5E%7B2%7D+%5Cbigg%5D+%5C%5C%5C%5C%5C%5C%5C%0A2.+%5Cdfrac%7B1%7D%7B2%7D%7E%7E+%5Cdisplaystyle%5Cint_%7B1%7D%5E%7B3%7D1.dx%5C%5C%5C%5C%5C%5C%5C%0A2.+%5Cdfrac%7B1%7D%7B2%7D%7E%7E+%5Cbigg%5Bx%5Cbigg%5D_%7B1%7D%5E%7B3%7D%5C%5C%5C%5C%5C%5C%5C%0A2.+%5Cdfrac%7B1%7D%7B2%7D%7E%7E+%5Cbigg%5B3-1%5Cbigg%5D%5C%5C%5C%5C%5C%5C%5C++%0A2.+%5Cdfrac%7B1%7D%7B2%7D%7E%7E+%5Cbigg%5B2%5Cbigg%5D%5C%5C%5C%5C%5C%5C%5C%0A%0A+++ "\displaystyle\int_{1}^{3}dx\bigg[2y\bigg]_{0} ^{1} \\\\\\\
2\displaystyle\int_{1}^{3}dx\bigg[ \frac{y^{2} }{2} \bigg]_{0} ^{1} \\\\\\\
2. \dfrac{1}{2}~~ \displaystyle\int_{1}^{3}dx\bigg[ y^{2} \bigg]_{0} ^{1} \\\\\\\
2. \dfrac{1}{2}~~ \displaystyle\int_{1}^{3}dx\bigg[ 1^{2} -0^{2} \bigg] \\\\\\\
2. \dfrac{1}{2}~~ \displaystyle\int_{1}^{3}1.dx\\\\\\\
2. \dfrac{1}{2}~~ \bigg[x\bigg]_{1}^{3}\\\\\\\
2. \dfrac{1}{2}~~ \bigg[3-1\bigg]\\\\\\\
2. \dfrac{1}{2}~~ \bigg[2\bigg]\\\\\\\")
Boa tarde!
Bons estudos!
Solução!
Boa tarde!
Bons estudos!
Respondido por
0
Resposta:
A alternativa correta é a: D.
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