7. Use cylindrical coordinates to evaluate S √x² + y² dx dy dz where S is bounded by Z= √√x² + y², z = 0, and x² + y² = 1.

Q: x-m+ 3x4+6x3 3x2 - 6x A B C — + x-1 x + 1 x+m +. dx. Find the sum of A, B, and C. D

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx A − cos(m− n)x+ · -cos(m+n)x] +…

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

Q: Evaluate tan" (x) sec4x dx. 1 1 A -tan 2) (x). + (m+2 -tan" (x) + C m+2 m (m+1) ¹) (x) (m- m+1 1…

A:

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

A: Given the spherical tank with diameter 4m So the radius of the spherical tank R = 2m Weight density…

Q: Given: 3z = xy Find fy O xy/3 Oy/3 Ox/3 O None of the choices

A: We can find the partial derivative as below

Q: Question 11 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: Explained below

Q: What is the value of f(1) - 16B in √ x³ Inx dx = f(x) ( (1/4) Inx - B) + C? О о O 3 02 01

A:

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

A:

Q: Consider s √(x- x-m+ 06 05 O 17/6 14/3 3x5 3x4+6x3-3x2 - 6x A B C + + x-1 x+1 x+m dx Using the…

A:

Q: Evaluate sin(1 sin (Inx) dx Integration by parts will be used repeatedly. What is the expression…

A: The objective is to find the right option.

Q: 3x5 S 3x4+6x³-3x2-6x x²-2x = 2 [ (x-1) 1/6 (x+2) 16/3 (x+1) 1/2 ® [ B x² - 4x 2 x-1) 1/6(x+2) 16/…

A:

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

A:

Q: Find S y dy y+2 using the substitution V +5=√y+2

A:

Q: Consider and C. -dx Using the method of partial fractions, the given integral can be written as…

A: Here, 3x53x4+6x3-3x2-6x=x-m+Ax-1+Bx+1+Cx+mor, x4x3+2x2-x-2=x-m+Ax-1+Bx+1+Cx+mor,…

Q: Stan" (x) sectx dx -tan (m + 1)(x). _¹_ -tan (m-1)(x) + C m+1 m-1 ¹__tan (™ + 2)(x) + —tan” (x) + C…

A:

Q: = fx²coss x²cosx dx- use integration by parts. What is the expression after the second integration…

A:

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: Consider 12-1 S= x-m+ 3x5 3x4+6x33x2 - 6x A B C + x-1 x + 1 x+m (A) 14/3 (B) 17/6 C) 5 6 —+ -dx.…

A:

Q: Evaluate A B Stan" (x) m+1 D "(x) sec4x dx. tan (+1)(x) +tan (-1)(x) + C m-1 tan (+1)(x)-tan (-1)(x)…

A: topic- indefinite integral

Q: Find the area bounded by the curve y=-x³ 1 - 16 A 8 square units B 16 square units 10 square units 4…

A:

Q: The integral [₁ face 8 dx S can be transformed to which of the following when trigonometric…

A: We have to solve above integral

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

A: Follow the procedure given below.

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

A:

Q: ·S- A 4u B [4-(2u²) ² C) -du V 4u Ⓒ* D -du 4 For x 1/2 -dx and using the substitution u=x1/2, the…

A: We have to solve above integral

Q: iven the vectors u = (8,5) and v = (-3,6), со (a) 6u (b) 7v - 2u (c) ||10u +3v||

A: Vector

Q: Suppose m and n are constants and m # n Evaluate O 1 1 -cos(m-n)x - - -cos(m+n)x] + C m-n m+n O 1 1…

A:

Q: Evaluate • O Stan" (x tan O m+1 1 m+3 1 m+2 m+1 "(x) sec¹x dx n (m + 1) (x) — __ ¹ (m+3)(x) + n (m +…

A:

Q: What is the value of f(1)-168 in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 2 B) 1 (C) D) 3

A:

Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B ) + C? O 0 01 2 со N 3 4

A:

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

A:

Q: 5ñ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=to x== 4 (A) 3.667…

A:

Q: What is the value of f(1)-16B in [x³ Inx dx = f(x) ((1/4) Inx-B) + C?

A: Please follow the next step.

Q: 53 3-2x-x²

A:

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

A:

Q: y dy √y+2 15. Find /y using the substitution u +5=√√y+2.

A:

Q: ‹S- A S Ⓡ /- © /- S- D For dx and using the substitution = x1/2, the resulting integral takes the…

A: Just use the substitution and find the required integral. Option (B) is correct.

Q: 3x5 Evaluate 3x4+6x3-3x2 - 6x ^ x² = 4x + 1 [ (x-1) 1/6 (x + 2) 16/3] + A In +C 2 1/2 16/3 B -2x-In…

A: Given that       ∫3x53x4+6x3-3x2-6xdx  We can re-structure this integral as…

Q: ·S= Evaluate 3x5 3x4+6x³-3x² - 6x + In x² - 4x 2 x² - 4x 2 x²-2x-In x² - 2x 2 -dx using method of…

A:

Q: . Given u = (-3,-4, -1), v = (6,2, -3), find (a) ||u|| (b) ||u+v|| u (c) u + v (d) u+v

A:

Q: QUESTION 5 Evaluate Sun"(x) seets de tan' ₁ (m + 2)(x) + tan m 1 -tan (m+3)(x) + · m+1 -tan…

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

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

A: We have to find out value

Q: Question 21 Consider S x-m+ 17/6 B 5 6 14/3 3x-5 3x4+6x3-3x2 - 6x A B C + + x-1 x+1 x + m -dx. Using…

A:

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

A: Solution is here

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

A:

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: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: Consider fx sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? (A) 1/4 B…

A:

Q: 4. What is the value of f(1) - 16B in § x³ Inx dx = f(x) ( (1/4) Inx - B ) + C? A. 0 B. 1 C. 2 D. 3

A: We know that integration of xn is xn+1/n+1.   Here i attached the solution of this question.

Q: Estimate the slope of the tangent line to the curve at the given point (-0.5,4.998) on the graph to…

A: It is clearly seen in the figure that the tangent line is horizontal to the x axis at the point…

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

A: