Expression 5: "z" equals 1 minus StartRoot, 1 minus "x" squared minus "y" squared , EndRoot left brace, "z" less than or equal to 1 half , right bracez=1−1−x2−y2z≤12
5
Expression 6: Start integral from 0 to 2 pi , end integral, Start integral from 0 to StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction , end integral, left parenthesis, StartFraction, "r" Over StartRoot, 3 , EndRoot , EndFraction minus left parenthesis, 1 minus StartRoot, 1 minus "r" squared , EndRoot , right parenthesis , right parenthesis "r" "d" "r" "d" theta∫2π0∫320r3−1−1−r2rdrdθ
equals=
0.2 6 1 7 9 9 3 8 7 7 9 90.261799387799
6
Expression 7: StartFraction, pi Over 12 , EndFractionπ12
equals=
0.2 6 1 7 9 9 3 8 7 7 9 90.261799387799
7
Expression 8: Start integral from 0 to 2 pi , end integral, Start integral from StartFraction, pi Over 3 , EndFraction to StartFraction, pi Over 2 , EndFraction , end integral, Start integral from 0 to 2cos phi , end integral, rho squared sine phi "d" rho "d" phi "d" theta∫2π0∫π2π3∫2cosϕ0ρ2sinϕdρdϕdθ
equals=
0.2 6 1 7 9 9 3 8 7 7 9 90.261799387799
8
Expression 9: rho equals 2cosine phiρ=2cosϕ
00
domain \theta Minimum:
less than or equal to theta less than or equal to≤θ≤
2 pi2π
domain \theta Maximum:
domain \phi Minimum: StartFraction, pi Over 3 , EndFractionπ3
less than or equal to phi less than or equal to≤ϕ≤
domain \phi Maximum: StartFraction, pi Over 2 , EndFractionπ2
