請問這題要怎麼解？（積分）

Evaluate the integrals in to integration by parts. 25. e√3s+9 dsimuzzA monood lon π/3

請問第25怎麼做？

Using Substitution Evaluate the integrals in Exercises 25-30 b to integration by parts. 25. 29v parts.w bonidmo od .1 eV3s+9 dsimuzzA29 26. eA. 9126. 90 S x 0 motorT [stnamebnu π/3 13 C

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

請教過程 謝謝🥲

the cos //dx. — sint ($) (3) + Evaluate X 5 I sin integrals

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

請問這題怎麼算，答案是2/e，感謝🙏

In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. (+01 *+∞d mine 15. •+∞0⁰) e -Vx Vx

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).