Given a ∈ [0, π / 2], then when ∫ a reaches the maximum value of 0 (cosx SiNx) DX, a=

Given a ∈ [0, π / 2], then when ∫ a reaches the maximum value of 0 (cosx SiNx) DX, a=

π/4
∫ a to 0 (cosx SiNx) DX = SiNx + cosx / A to 0 = Sina + cosa-1
On a ∈ [0, π / 2], the maximum is obtained when a = π / 4

Given that a > 0, when ∫ (cosx SiNx) DX (upper limit a, lower limit o) is the maximum, the minimum value of a is 0___________ (detailed process is required.)

∫ [0 - > A) (cosx SiNx) DX = cosx + SiNx (0 - > A) = cosa + sina-cos0-sin0 = cosa + sina-1, Let f (a) = cosa + sina-1 = √ 2 * sin (a + π / 4) - 1, when sin (a + π / 4) = 1A + π / 4 = π / 2A = π / 4, f (a) has the maximum value, and the maximum value is f (π / 4) = √ 2 * sin (...)

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

∫(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