For the solid S shown below, the of \int\int_{s}\int x d x d y d z (rounded off to two decimal places ) is

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 57 of 65

Marks: +1, -0

For the solid S shown below, the of

∫∫↙{s}∫ x d x d y d z

(rounded off to two decimal places ) is

Solution:

From the figure

X=0 \;\text " to "\; 3 .

Y=0 \;\text " to "\; 1

Z=0 \;\text " to "\; 1-Y

=∫↙{0}↖{3} ∫↙{0}↖{1} ∫↙{0}↖{Y-1} X d Z d Y d X

=∫↙{0}↖{3} ∫↙{0}↖{1} X(Z) d Y d X

=∫↙{0}↖{3} ∫↙{0}↖{1} X(1-Y) d Y d X

=∫↙{0}↖{3} X(Y-\;{Y^{2}}/{2})|_{0} ^{1} d X

=∫↙{0}↖{3} × \;{1}/{2} d x

=\;{x^{2}}/{4}|_{0} ^{3}=\;{9}/{4}=2.25

Go to Question:

Prev Question

Next Question