4 / | | / 2 2 \ | \x + y + 1/ dy | / _________ / 2 \/ 16 - x
Integral(x^2 + y^2 + 1, (y, sqrt(16 - x^2), 4))
Integrate term-by-term:
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
The integral of is when :
The result is:
The integral of a constant is the constant times the variable of integration:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 3 | / 2 2 \ y 2 | \x + y + 1/ dy = C + y + -- + y*x | 3 /
3/2 / 2\ _________ 76 2 \16 - x / / 2 / 2\ -- + 4*x - ------------ - \/ 16 - x *\1 + x / 3 3
=
3/2 / 2\ _________ 76 2 \16 - x / / 2 / 2\ -- + 4*x - ------------ - \/ 16 - x *\1 + x / 3 3
76/3 + 4*x^2 - (16 - x^2)^(3/2)/3 - sqrt(16 - x^2)*(1 + x^2)
Use the examples entering the upper and lower limits of integration.