∫ (- pi / 2 부터 pi / 2 까지) (cos ^ 2x + 8) dx (- 4 ~ 0) | x + 3 | dx

∫ (- pi / 2 부터 pi / 2 까지) (cos ^ 2x + 8) dx (- 4 ~ 0) | x + 3 | dx


∫ (- pi / 2 → pi / 2) (cos & # 178; 2x + 8) dx
= ∫ (0 → pi / 2) (1 + 코스 4x) dx + 8 ∫ (- pi / 2 → pi / 2) dx
= (x + 1 / 4 * sin4x) | (0 → pi / 2) + 8 pi
= pi / 2 + 8 pi
= 17 pi / 2
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x + 3 = 0, x 8712 ° [- 4, 0]
= > x = - 3
x 8712 ° [- 4, - 3], x + 3 < 0
x 8712 ° [- 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