作业帮∫（-π/2到π/2)(cos^2x+8)dx ∫(-4到0)|x+3|dx
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∫（-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到π/2)(cos^2x+8)dx ∫(-4到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
1）
∫（-π/2到π/2)(cos^2x+8)dx
=∫（-π/2到π/2)[(1+cos 2x)/2 +8] dx
=∫（-π/2到π/2)[1/2 + 0.5 cos 2x + 8] dx
=∫（-π/2到π/2)(8.5 + 0.5 cos 2x ) dx
=8.5π + 0.5∫（-π/2到π/2) cos 2x dx
=8.5π + 0....
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1）
∫（-π/2到π/2)(cos^2x+8)dx
=∫（-π/2到π/2)[(1+cos 2x)/2 +8] dx
=∫（-π/2到π/2)[1/2 + 0.5 cos 2x + 8] dx
=∫（-π/2到π/2)(8.5 + 0.5 cos 2x ) dx
=8.5π + 0.5∫（-π/2到π/2) cos 2x dx
=8.5π + 0.25∫（-π/2到π/2) cos 2x d(2x)
=8.5π + 0.25×0
＝8.5π
2）
∫(-4 -> 0)|x+3|dx
=-∫(-4 -> -3)(x+3)dx + ∫(-3 -> 0)(x+3)dx
=-[(-3+3)²/2-(-4+3)²/2] + [(0+3)²/2-(-3+3)²/2]
=-(0-1/2)+(9/2-0)
= 5
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