QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5) 2²=2y, the x-axis, and the line tangent to the circle x² + y²=25 at (3,4). 33.43 square units 43.23 square units 22.89 square units 15.21 square units

Q: Suppose m and n are constants and m‡n. Evaluate [sin(mx) sin (mx) cos(nx) dx 1 _____cos (mn)x -…

A: We have to solve integration

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: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: Question 14 π 5ñ Find the area bounded by the trigonometric curves y = sinx and y=cosx from x = —to…

A:

Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

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

A:

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

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Q: ·S- For x1/2 S- S. dx and using the substitution -du U 1-u² 4u -du 4u 4- (21²) ² U -du 1-u4 -du u=x…

A: We have to solve Integral

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

A: Here we have to find the area bounded by the given trigonometric curves.

Q: dx 3-2x-x2

A: Since, the student has posted multiple questions and mentioned to solve no. 5 but there is no no. 5…

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

A:

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

A:

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

A:

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

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Q: x1/2 ·S. dx and using the substitution = x1/2, the resulting integral takes the form: U (A) / -du…

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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: valuate A B C (D) Stan" (x tan" (x) sec4x dx. 1 -tan (m + 3)(x) +_¹__tan -tan (m + ¹)(x) + C 1) m+3…

A:

Q: Question 8 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: Solved below.

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

A:

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: 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: S x dx x²+√√x²-1-1 The integral substitution? (A) [sec²0d0 1+tan cose de (B) 1-sine sece tane de…

A: Simplify and substitute x = sec θ to get the answer.

Q: Evaluate A B D Stan" (x) sec¹x dx. 1 (m+1 ¹) (x) + m+1 1 )(x) + m+3 2) (x) + m+2 -¹)(x) – m+1 tan…

A: We will evaluate the given integral by using substitution method as shown below

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

A: Follow the procedure given below.

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

A: Solution is here

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

A:

Q: QUESTION 8 Consider S S[x_m+ 17/6 5 6 14/3 3x5 -dx- Using the method of partial fractions, the given…

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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: Given :Region bounded by x2=4y and y2=4xRevolving about y=4

Q: Consider x-m+ A 17/6 B 14/3 с 6 3x5 3x4+6x3 3x2 - 6x A B C + + x-1 x+1 x+m -dx. Using the method of…

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Q: Question 11 Evaluate €S= A B C D 3x5 3x4+6x³-3x² - 6x x²-2x-In x² - 4x 2 x² - 2x 2 x² - 4x + In +…

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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: What is the solution to the differential equation 2√√ay- da Oy = ( ² √₂-2) ? 3 Oy=(2²√x - 2) ³ 1 =…

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Q: ·S- y dy √y+2 using the substitution u +5=√√y+2. A(√3+2-5)(-5√y+2+y+21) +C B (√y+2-5) (5√3+2-y+24)…

A:

Q: 6 "Cosx dx. Sinx+25inx+5

A: Integration by Trigonometric substitution:

Q: Find the area bounded by the curve y=x³x²+3x and the line y=x. 16 (A) 8 square units (B) 4 square…

A:

Q: QUESTION 7 Evaluate 3x5 3x4+6x³-3x² - 6x x²-2x-In O x²-4x 2 O x²-4x 2 O rẻ-2r 2 [(x-1) 1/6(x+2) 16/3…

A:

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: 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…

A:

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

A:

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

A:

Q: Evaluate S= 3x5 3x4+6x33x2 - 6x + In O x-2 2 x² - 4x 2 O x² - 4x + In 2 x²-2x-In + In -dx using…

A: Given problem:-

Q: QUESTION 14 I 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x==…

A: Find area between two curve

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

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Q: S- Find y dy Vy+2 using the substitution u +5=√√x+2. A ²/ (√x+2-5) (-5√/y+2+y+21)+C ℗ ²/(√√y+2-5)…

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Q: Consider √(x-m. 3x5 -dx. Using the method of partial fractions, the given integral can be written as…

A:

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

A: using circular ring method evaluate the volume

Q: R 5″ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=- 4 4 (A…

A: Here we have to find the area bounded by the given trigonometric curves.