∫ (- π / 2 to π / 2) (COS ^ 2x + 8) DX ∫ (- 4 to 0) | x + 3| DX | Math enthusiast | Mathematical art

∫ (- π / 2 to π / 2) (COS ^ 2x + 8) DX ∫ (- 4 to 0) | x + 3| DX

∫(-π/2→π/2) (cos²2x + 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
_______________________
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

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