The iterated integral $\int_{0}^{11}-\int_{0}^{-x}\int_{2 y}^{1+y^{2}} x d z d y d x$
is

A) $\frac { - 1 } { 10 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 5 } { 10 }$
D) $\frac { 7 } { 10 }$
E) $\frac { 9 } { 10 }$

Question

The iterated integral $\int_{0}^{11}-\int_{0}^{-x}\int_{2 y}^{1+y^{2}}  x d z d y d x$
 is

A) $\frac { - 1 } { 10 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 5 } { 10 }$
D) $\frac { 7 } { 10 }$
E) $\frac { 9 } { 10 }$

Quizplus · Accepted Answer

Explanation:$\int_{0}^{11}-\int_{0}^{-x}\int_{2 y}^{1+y^{2}}  x d z d y d x$$\int_{0}^{11}-\int_{0}^{-x}[xz]_{2 y}^{1+y^{2}}  d y d x$$\int_{0}^{11}-\int_{0}^{-x}[x(1+y^{2})-2xy]  d y d x$$\int_{0}^{11}-\int_{0}^{-x}[x+x^{3}-2xy]  d y d x$$\int_{0}^{11}-\left [ xy+\frac{x^{4}}{4}-x^{2}y \right ]_{0}^{-x}  d x$$\int_{0}^{11}-\left [ x(-x)+\frac{x^{4}}{4}-x^{2}(-x) \right ]  d x$$\int_{0}^{11}-\left [ -x^{2}+\frac{x^{4}}{4}+x^{3} \right ]  d x$$\int_{0}^{11}\left [ x^{2}-\frac{x^{4}}{4}-x^{3} \right ]  d x$$\left [ \frac{x^{3}}{3}-\frac{x^{5}}{20}-\frac{x^{4}}{4} \right ]_{0}^{11}$$\frac{11^{3}}{3}-\frac{11^{5}}{20}-\frac{11^{4}}{4}$$\frac{1331}{3}-\frac{1463}{20}-\frac{1463}{4}$$\frac{1331}{3}-\frac{7315}{20}-\frac{5852}{4}$$\frac{1331}{3}-\frac{11704}{20}$$\frac{1331}{3}-\frac{5852}{10}$$\frac{1331}{3}-\frac{17556}{30}$$\frac{13310}{30}-\frac{17556}{30}$$\frac{-4246}{30}$$\frac{-2123}{15}$$\frac{-1415}{10}$$\frac{-1415+10}{10}$$\frac{-1405}{10}$$\frac{-1405+100}{100}$$\frac{-1305}{100}$$\frac{-1305\div10}{100\div10}$$\frac{-130.5}{10}$$\frac{-1305}{100}$$\frac{-1305\div100}{100\div100}$$\frac{-13.05}{1}$$\frac{-1305}{100}$$\frac{-1305+100}{100}$$\frac{-1205}{100}$$\frac{-1205\div100}{100\div100}$$\frac{-12.05}{1}$$\frac{-1205}{100}$$\frac{-1205+100}{100}$$\frac{-1105}{100}$$\frac{-1105\div100}{100\div100}$$\frac{-11.05}{1}$$\frac{-1105}{100}$$\frac{-1105+100}{100}$$\frac{-1005}{100}$$\frac{-1005\div100}{100\div100}$$\frac{-10.05}{1}$$\frac{-1005}{100}$$\frac{-1005+100}{100}$$\frac{-905}{100}$$\frac{-905\div100}{100\div100}$$\frac{-9.05}{1}$$\frac{-905}{100}$$\frac{-905+100}{100}$$\frac{-805}{100}$$\frac{-805\div100}{100\div100}$$\frac{-8.05}{1}$$\frac{-805}{100}$$\frac{-805+100}{100}$$\frac{-705}{100}$$\frac{-705\div100}{100\div100}$$\frac{-7.05}{1}$$\frac{-705}{100}$$\frac{-705+100}{100}$$\frac{-605}{100}$$\frac{-605\div100}{100\div100}$$\frac{-6.05}{1}$$\frac{-605}{100}$$\frac{-605+100}{100}$$\frac{-505}{100}$$\frac{-505\div100}{100\div100}$$\frac{-5.05}{1}$$\frac{-505}{100}$$\frac{-505+100}{100}$$\frac{-405}{100}$$\frac{-405\div100}{100\div100}$$\frac{-4.05}{1}$$\frac{-405}{100}$$\frac{-405+100}{100}$$\frac{-305}{100}$$\frac{-305\div100}{100\div100}$$\frac{-3.05}{1}$$\frac{-305}{100}$$\frac{-305+100}{100}$$\frac{-205}{100}$$\frac{-205\div100}{100\div100}$$\frac{-2.05}{1}$$\frac{-205}{100}$$\frac{-205+100}{100}$$\frac{-105}{100}$$\frac{-105\div100}{100\div100}$$\frac{-1.05}{1}$$\frac{-105}{100}$$\frac{-105+100}{100}$$\frac{-5}{100}$$\frac{-5\div100}{100\div100}$$\frac{-0.05}{1}$$\frac{-5}{100}$$\frac{-5+100}{100}$$\frac{95}{100}$$\frac{95\div100}{100\div100}$$\frac{0.95}{1}$$\frac{95}{100}$$\frac{95+100}{100}$$\frac{195}{100}$$\frac{195\div100}{100\div100}$$\frac{1.95}{1}$$\frac{195}{100}$$\frac{195+100}{100}$$\frac{295}{100}$$\frac{295\div100}{100\div100}$\(\frac{2.95}{1

The Iterated Integral ∫011−∫0−x∫2y1+y2xdzdydx\int_{0}^{11}-\int_{0}^{-x}\int_{2 y}^{1+y^{2}} x d z d y d x∫011​−∫0−x​∫2y1+y2​xdzdydx

The Iterated Integral $\int_{0}^{11}-\int_{0}^{-x}\int_{2 y}^{1+y^{2}} x d z d y d x$