Anonymous
Anonymous asked in 教育與參考考試 · 1 decade ago

三角函數積分問題。

積分9/2cos^2x的答案。

因為我數學不太好,

所以答案請附詳解,謝謝。

1 Answer

Rating
  • linch
    Lv 7
    1 decade ago
    Favorite Answer

    ∫9/(2 cos^2 x) dx = (9/2)∫sec^2 x dx = (9/2) tan x + C

    Hint: sec x = 1/cos x, ∫sec^2 x dx = tan x + C

    若題目是

    ∫(9/2) cos^2 x dx = (9/2)∫(1 + cos 2x )/2 dx = (9/2) (x/2 + sin 2x /4) + C

    = (18x + 9sin 2x) / 8 + C

    Hint: cos^2 x = (1 + cos2x) / 2

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