Answer to Question #219583 in Calculus for Rehema

Question

evaluate

$\int_{y=1}^2\int_{x=0}^3(1+8xy)dxdy$

Answer 1

ANSWER:$\int _{ y=1 }^{ 2 }{ \int _{ x=0 }^{ 3 }{ \left( 1+8xy \right) dxdy } } =\ 57$

EXPLANATION.

Since $\int _{ x=0 }^{ 3 }{ \left( 1+8xy \right) dx\ } =\ \int _{ x=0 }^{ 3 }{ dx } +8y\int _{ x=0 }^{ 3 }{ xdx } =3+8y{ \left( \frac { { x }^{ 2 } }{ 2 } \right) }_{ x=0 }^{ 3 }\ =3+\ 36y$ , then $\int _{ y=1 }^{ 2 }{ \int _{ x=0 }^{ 3 }{ \left( 1+8xy \right) dxdy } } =\int _{ y=1 }^{ 2 }{ (3+\ 36y)dy } = { \left( 3y+18{ y }^{ 2 } \right) }_{ 1 }^{ 2 }=6+18\cdot 4-3-18=57\\$