Question

∫√x^2+y^2 dx

求 ∫(0→a) dx ∫(0→x) √(x^2+y^2)
∫(0→a) dx ∫(0→x) √(x^2+y^2) dy

Answer 1

∫(0→a) dx ∫(0→x) √(x^2+y^2) dy
=∫(0→a)(x²y+y³/3)|(0→x)dx
=∫(0→a)(x³+x³/3)dx
=∫(0→a)(4x³/3)dx
=(x^4)/3|(0→a)
=(a^4)/3