∫(-π/2到π/2)(cos^2x+8)dx∫(-4到0)|x+3|dx

∫(-π/2到π/2)(cos^2x+8)dx∫(-4到0)|x+3|dx


∫(-π/2→π/2)(cos²;2x + 8)dx
=∫(0→π/2)(1 + cos4x)dx + 8∫(-π/2→π/2)dx
=(x + 1/4*sin4x)|(0→π/2)+ 8π
=π/2 + 8π
= 17π/2
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x + 3 = 0,x∈[-4,0]
=> x = -3
x∈[-4,-3],x + 3 < 0
x∈[-3,0],x + 3 > 0
∫(-4→0)|x + 3| dx
=∫(-4→-3)-(x + 3)dx +∫(-3→0)(x + 3)dx
= 1/2 + 9/2
= 5