Evaluate 3x5 3x4+6x3-3x2 - 6x S= -dx, using method of partial fractions.

Q: What is the solution to the following initial value problem? dy + 4x = 3 y(0) = 1 da Oy=-2x² + 3x -…

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Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

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…

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Q: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

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Q: x1/2 S dx and using the substitution = x 1/2, the resulting integral takes the form: x-x³ U A / du U…

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Q: [sin(mx) cos(nx) dx 9. Suppose m and n are constants and m #n. Evaluate 1 1 -cos(m− n)x+ -cos(m+n)x…

A: Evaluate the integral

Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=—. 4 4 (A)…

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

Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y, the…

A: Solution of the problem as follows

Q: Л 5л nd the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-. 4 4

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx 1 1 1 [1 -cos(m− n)x= cos(m+n)x]…

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

A: Here is the solution of the given problem. Method of Partial Decomposition

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

A: Given

Q: What is the derivative of the following? sin(t) d dt f 117 da cos(t) s(t) 4-sin² (t) 1 4 — sin² (t)…

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Q: QUESTION 4 Evaluate › [ sin(lnx) dx' Integration by parts will be used repeatedly. What is the…

A: Integration by parts

Q: Exercises To Solve [No.5] 3-2x-x²

A: Solved below.

Q: Consider S integral can be written as of A, B, and C. 6 O 5 14/3 O 17/6 3x5 3x4+6x3-3x2 - 6x √(x-1…

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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 to…

A: Solution is here

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

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

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

A: We need to integrate the given function with integration by parts.   We will do it twice

Q: 10. The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4…

A: The region bounded by the given curves x2=4y & y2=4x is: which is rotated around y=4.

Q: Exercises To Solve [NO.5] D "Cosx dx. Sinx+25inx+5 6 3 b

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

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Q: 3x5 S= -dx. Using the method of partial fractions, the given integral can be written as…

A: Solution: ∫x53x4+6x3-3x2-6xdx

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

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

A: Given that ∫x sinx cosx dx=fxsin2x-gxcos2x+C

Q: QUESTION 15 Evaluate sin(Inx) dx Integration by parts will be used repeatedly. What is the…

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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: Evaluate 1 m+2 tan" (x) sec4x dx n (m + 2)(x) + — tan" (x) + C tan m 1 -tan (m+3)(x). ī -tan…

A: Solution is here

Q: fe²x+lnx² sin x² dx = 25-410-312-2 2M 12 e2x cos x² dx

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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 to…

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Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

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Q: Let f(x) = 8x³ - 4. What is the value of c on the interval [0,2], such that f(c) equals the average…

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Q: Evaluate tan" (x) secx dx. 1 A n(m + 1)(x). m+1 1 (В -tan (m + 2)(x) + m+2 1 -tan (m+1)(x). m+1 1…

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Q: The integral B D x dx can be transformed to which of the following using trigonometric substitution?…

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Q: S sec²0 do 1+tano seco tane de seco - 1 The integral O 1: S S x dx x²+√√√x²-1-1 coso do 1-sino sino…

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

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Q: Find S- y dy using the substitution u +5=√y+2. y+2 (A) (√3+2-5) (5√/F+2-1+24) +C 3 B…

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A 1/2 B…

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Q: x dx ·S- can be transformed to which of the following using trigonometric substitution? x²+√√x²-1-1…

A: Trigonometric substitution

Q: y dy Find S² using the substitution u +5=√y+2. √y+2 (A) (√3+2-5) (5√3+2+y+21) +C 3…

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Q: 24) + C

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Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

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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 to…

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

Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

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

A: We have to find the solutions