求解第四題的旋轉體表面積（繞y軸）

revolving the given curve about the indicated Tb. Graph the curve to see what it looks ke. If the surface too. T c. Use your utility's integral evaluator to find t numerically. 1. y = tan x, 0 ≤ x ≤ π/4; x-axis 2. y = 3. xy = 1, 1 ≤ y ≤ 2; x², 0 ≤ x ≤ 2; x-axis y-axis V 4. x = sin y, 0 ≤ y ≤ π; y-axis 5. x1/2 + y1/2 = 3 from (4, 1) to (1, 4); x-axis 6. y + 2√y = x, 1 ≤ y ≤ 2; 7x=siny Ct y-axis

請問第45題要怎麼解🙏

45-45 Evaluate the int 43-45 Evaluate the integral by changing to spherical coordinates. 43 1 √1-x² √√2-x²-y² √√√√x² + y² xy dz dy dx Jo langsini plan zorami par orige bilo svo langoni siqu sign X (49) S² √²-² √223²23² (x²z + y²z + z³) dz dx dy 44% Sva Toni -a -√√a²-y² J-√a²-x²-y² lo smulov sd tarb wore of as broos Iasibailys (n) .12 (2 2+√4-x²-y² 45, 1³²₂ √√²=x²² √² + √²=x²=3² (x² + y² + 2²j3/2 dz dy dx blows √2-√√4-x²-y² 1001=1 onoo ori yd wolad

請問這題要怎麼解🙏🙏

integrals.OITUOate that the (a) Soº 1-11-8 11-8-30 x²e-x² dx 0

31&35都是不存在 不存在要如何判斷

adrant adrant Evaluate the following improper integrals: x dx 28. dx 广 1 29. = -2 (x² – 4) 3x vertical 2 X 30. dx 31. 1.0 • dx (9 - x2) ? x - 1 x² dx 32. si 33. (x – 8) 3 dx (x - 3)2/5 - | r 5 X 1 34. dx 35. dx (x² – 4)² -3 (x + 2)4

9）想問中間值那個什麼的是怎麼算？ 網路上的定義搜不到 謝謝

9-12 Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. *10 1/2 9. 8,5°/x3 + 1dx, n=4 , 10. ("* cos*x dx, n= 4 4 12 JO

作業寫不出來😭微積分

if (x, y) = (0,0) ( 20 points ) Let f(x, y) = x²y² x4 + y + 0, if (x,y) = (0,0) (a) Does lim f(x,y) exist ? Give reasons. (x,y) → (0,0) (b ) Find the partial derivatives fx(0,0) and fy(0,0).

大一微積分 求求大家幫忙🙏🏻😭

(b ) Find the radius of convergence and interval of convergence of the power series Enzo (-1)n (2x + 3)n 2n

力學 救救我 謝謝！（第三題不用）

1. Considerathin rod ofuniform linear mass density pL with mass 4/ and length /, find the gravitational potential。dp/有)。at a perpendicular distance Afrom the center ofthe rod. You may find the integral in (E.6) in Appendix E useful 2. A spherical planet of radius 人> consists ofacore of radius 有/ with uniform density pi. and a thick outer cloud of dust with umiform density p: Find the force (magnitude and direction) onamass箇inside the dust cloud ata position ARp from the planetcenter( 吃<訪<記), 3. Use Fermat's principle by applying calculus of variation to minimize the time oflight passing from medium ofrefractive index jg, to another medium ofrefractive index >, derive the Snells law ofrefraction: js光 名2s 銷 4. Consider the Atwood machine oftwo masses connected by amassless string oflength 7overapulley ofradius gas shown, (a) Write down the total kinetic energy and potential energy in terms of the coordinatex Hence obtain the Lagrangian ofthe system. (b) Derive the Lagrange's equation of motion and hence find the acceleration ofthe masses. x 和二 工

求解ಠ_ಠʕ •ᴥ•ʔ 微積分～

Find the indefinlte integraL: Jie 必

求解 二重積分 已畫出範圍 但無法得出正確答案 會用到Jacobian變數代換嗎？ 謝謝

8. 本valuate the double integral] 二人 二 ] 0 Z2 十 2 和 白9. dZZZ?/ 十 了 1