Evaluate the following iterated integrals. int_0^3int_{-2}^1 (2x+3y)dxdy

Question
Integrals
asked 2021-03-02
Evaluate the following iterated integrals.
\(\int_0^3\int_{-2}^1 (2x+3y)dxdy\)

Answers (1)

2021-03-03
\(\text{Given integral,}\)
\(\int_0^3\int_{-2}^1 (2x+3y)dxdy\)
\(\text{Now}\)
\(\int_0^3\int_{-2}^1 (2x+3y)dxdy=\int_0^3(\frac{2x^2}{2}+3xy)_{-2}^1 dy\)
\(=\int_0^3 (x^2+3xy)_{-2}^1 dy\)
\(=\int_0^3 ((1)^2+3(1)y-(-2)^2-3(-2)y)dy\)
\(=\int_0^3 (1+3y-4+6y)dy\)
\(=\int_0^3 (-3+9y)dy\)
\(=(-3y+\frac{9y^2}{2})_0^3\)
\(=(-3(3)+\frac{9(3)^2}{2}+3(0)+\frac{9(0)^2}{2})\)
\(=-9+\frac{81}{2}+0\)
\(=\frac{63}{2}\)
\(\text{Final answer:}\)
\(\int_0^3\int_{-2}^1 (2x+3y)dxdy=\frac{63}{2}\)
0

Relevant Questions

asked 2021-01-31
Evaluate the following iterated integrals.
\(\int_0^2\int_0^1\frac{8xy}{1+x^4}dxdy\)
asked 2021-02-25
Evaluate the following iterated integrals.
\(\int_0^2\int_0^1 4xy\ dx\ dy\)
asked 2021-02-12
Evaluate the following integrals.
\(\int_0^3\frac{2x-1}{x+1}\)
asked 2021-01-10
Evaluate the following iterated integrals.
\(\int_1^2\int_0^1(3x^2+4y^3)dydx\)
asked 2021-03-09
Evaluate the following integrals.
\(\int_0^1\frac{16^x}{4^{2x}}dx\)
asked 2021-01-28
Evaluate the following iterated integrals. \(\int_1^3\int_1^2(y^2+y)dx\ dy\)
asked 2021-01-08
Evaluate the following iterated integrals.
\(\int_1^3\int_0^{\pi/2}x\sin y\ dy\ dx\)
asked 2021-02-06
Evaluate the following integrals.
\(\int_0^{\pi/2}4^{\sin x}\cos xdx\)
asked 2020-11-01
Evaluate the following integrals.
\(\int_{\ln2}^{\ln3}\frac{e^x+e^{-x}}{e^{2x}-2+e^{-2x}}dx\)
asked 2021-01-13
Evaluate the following integrals. Include absolute values only when needed.
\(\int\frac{\ln^2x+2\ln x-1}{x}dx\)
...