Question

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

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

Answers (1)

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