七、請利用= cosx。（15 分）

(二)並計算定積分面積。（6 分）

(一)試求以上兩曲線方程式，繞著 x 軸旋轉轉動之物體體積。 （10 分）

(二)試求以上兩曲線方程式，繞著y = 6直線軸旋轉轉動之物體體積。（10 分）

六、試利用分部積分法，求不定積分。（15 分） 

一、中譯英：（15 分）現代人的平均壽命較過去長，因此對於退休生活的規劃成為一件重要的事情。據說，人們若是在沒有準備好的情況下退休，會很容易感到生活中頓時多出許多時間，他們很容易會不知道每天該做些什麼。由於生活 重心的突然改變，讓人們可能會產生放空狀態，一下子老的很快、思考和行動都可能變得呆滯，也正因為這種現象很普遍，讓很多人更加有所警惕。

二、英譯中：（15 分）People attend university for different reasons. Before applying for university admission, young people must ask themselves what they want from their target universities and what they want to do after graduation. Many people attend top universities because of the prestige without considering their choices of future career. If a person has interest in a certain career, he/she should find universities with a better reputation for such a career choice. With a degree from a university that is most respected in the profession one wants to enter, it will be easy for the person to get his/her dream job and climb the career ladder fast.

三、英文作文：（20 分）In 2023, finally, COVID-19 has gradually become a term that no longer bears much threat to people’s lives. In many aspects, people’s lives have returned to the situations three years ago. The tourism industry has witnessed a sharp growth in the past few months. Moreover, many academic exchanges have resumed. Yet, some changes will not disappear that fast. Please write a 200-word essay focusing on the lingering impacts of the pandemic.

(一)請問此新開發藥物對減少梗塞面積有顯著減少嗎？請以單尾檢定進行分析，並報告p值。（10分）

(二)如果接受此新開發藥物治療的族群患者真實的平均梗塞面積為 20(ck-g-EQ/m2)，且σ=10(ck-g-EQ/m2)，請以單尾檢定計算此檢定的檢力（power）。（15分）（備註：P(Z≥0.23)=0.409，P(Z≥1.645)=0.05，P(Z≥1.96)=0.025， P(Z≥2.55)=0.005）

二、假設有藥商宣稱其新產品的藥物在治療高血壓的有效率為80%，今實際試驗500位高血壓患者，結果有375位高血壓患者在服用後血壓控制為 正常，若欲檢測實際的試驗結果是否與藥商所宣稱的效果相符合，請進行檢定。（20分）（備註：）