Find 36 zdV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), and (0,0,2) E

Q: dx The integral ·S= can be transformed to which of the following when trigonometric substitution is…

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: I 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x = - 4 4 1.414…

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Q: What is the value of f(1)- 168 in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 3 B 0 1 2

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Q: 24) + C

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Q: Find y dy ·S using the substitution u +5=√√y+2 y+2 © ²(√√y+2-5) (5√/y+2+y+24) + C…

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Q: QUESTION 15 Find the area bounded by the curve y = 16 4 square units 16 square units 10 square units…

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Q: waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan”…

A: We will evaluate the given integral as shown below

Q: Question 2 S y dy Find √x+2 A ² (√x+2-5) (5√/y+2+y+24) + C 3 ℗ ²² (√5+2-5) (5√/y+2+y+21) + C B…

A: GIVEN

Q: Previous question Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and…

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Q: What is the value of 1)- 168 in x² Inx dir = f(x) ( (1/4) Inx-8) + C? 03

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Q: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2 = 4x about y=4 is…

A: The full solution of the question is given below:

Q: dx The integral ·S= can be transformed to which of the following when trigonometric substitution is…

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Q: Consideri x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 3/8 1/4…

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Q: For f x 1/2 dx and using the substitution=x1/2, the resulting integral takes the form: -du 411…

A: We know that integration of xn is nxn-1.   Here i attached the solution of this question.

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y² = 4x about y = 4…

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Q: Secor, x²cosx dx use integration by parts. What is the expression after the second integration by…

A: We have  to solve above integral

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

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Q: өpapzp4=6,ff f f +

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Q: The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by…

A: Given,The temperature. H. in degrees Celsius, of a cup of coffee placed on the kitchen counter is…

Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

A: Integration by Trigonometric substitution.

Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

Q: af Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

Q: A -2 f Coxx dx x’sinx + 2x cosx – 2 dx + C

A: Using integration by parts,we got correct answer as option -(A)

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: -dx, using method of partial 5x /6(x+2) 16/3 +1) 1/2 ] 6(x+2) 16/3- 1) 1/2 16/]+C с 16(x+2) 16/3 +C…

A: We have to choose the correct option from the given options according to the given information

Q: To evaluate [x²cosx dx. use integration by parts. What is the expression after the second…

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Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: -S- A Ⓡ / T B C S (D) S- For x1/2 dx and using the substitution u=x¹ x1/2, the resulting integral…

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Q: Find the area bounded by the trigonometric curves 3.667 square units 2.828 square units 3.459 square…

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Q: Evaluate sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

A: we have to find the solution

Q: Evaluate x2— 2x = In 4x–ܐ0x 3 5 3x4+ 63 - 3x2 -— 6x 2 O,2-4x 2 0 x²-2x 2 + ܀ -dx using method of…

A: Let's evaluate given integral.

Q: Exercises To Solve [No.5] 6 "Cosx dx. Sin²x+25inx+5

A: Here is the solution

Q: Question 1 A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³).…

A: We need to find the integral for work done in pumping the content to a point 3m  from the top of…

Q: QUESTION 19 A trough is full of liquid of weight density 9,000 N/m3. The ends of the trough are…

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Q: find the value of k that will make the function continuous. f(x)= { 2        ,if x <-4         { -x…

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y² = 4x about y = 4…

A: Using circular ring method about y=4 find outer and inner radius then evaluate volume

Q: b The volume of the solid generated by revolving the region bounded by x2-4y and y2-4x about y=4 is…

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Q: QUESTION 19 A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are…

A: Solution of the problem as follows

Q: QUESTION 1 Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?…

A: Topic = Integration

Q: Evaluate (A) (В B D Stan" (x) see4x dx- 1 m+3 -tan (m+3)(x) + m+1 1 (m+1 1 tan + ¹)(x) − − m+1 m-1 1…

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Q: aluate A B Ⓒ D Stan™ tan" (x) sec¹x dx. 1 M+2 - 777 +1 - tan tan (m + 1)(x) + tan (m + 1)(x) -tan…

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Q: For x 1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: 4u -du 4-u U…

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Q: S √(x-m+ 3. Consider 3x5 3x4+6x3-3x² - 6x A B C + + x-1 x+1 x+m -dx. Using the method of partial…

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Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: Given:         Density of Liquid ρ=9000 N/m3          Sides of triangle a=2 m     The expression for…

Q: Question 13 The integral dx √(x²+4)² c'e ³0 do sin²0 de Ⓒ-csc³0 Ⓒos²0 csc ³0 de cos¹0 de can be…

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Q: Find S y dy Vy+2 D using the substitution u + 5 = √y+2. A √y+2−5) (5√√y+2+y+24) + C Ⓡ(√9+2-5)…

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Q: y dy Find S y+2 O / (√x+2-5) (5√/y+2+y+24) + C 3 O (√y+2-5) (-5√3+2+y+21)+C 3 (√y+2-5)…

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