y= (4x² + 2) (4x3³ - x)

Q: Question 21 y dy Find y+2 using the substitution +5= √y+2.

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

A: We have to find the radius of inner circle

Q: y dy Find 13 using the substitution +5=√y+2. √y+2 A ²/ (√x+2-5) (5√/y+2-y+24) + C 3 B (√9+2-5)…

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

A: Given :(x+5)2=2y, the x-axis, and the line tangent to the circle x2+y2=25 at (3,4).To find :The area…

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

A: Given ∫sin (ln x) dx Let I=∫sin (ln x) dx By using integration by parts method,∫udv=uv-∫vdu u= sin…

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: A particle is moving with acceleration a(t) = 30t + 8. its position at time t = 0 is s(0) velocity…

A: topic- integration

Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1…

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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…

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

A: solution

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: Find y dy ·S= using the substitution u +5=√√y+21 Vy+2 ²/(√√y+2-5) (5√√y+2+y+24) +C…

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

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Q: Exercises To Solve [No.5] 3-2x-x²

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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: 20. [(x²+2x-10/3 (5x+5)dx

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Q: substitutionu +5=√y+2. -5√/y+2+y+21)+C 5√y+2=y+24)+C

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

Q: True/False 1) d[f(x) g(x)]/dx= f'(x)/g'(x) 2) d[f(x)]"/dx= n[f(x)] f'(x) and…

A: This question is based on diffrentiation and integration.

Q: Find the area bounded by the curve 4 square units 10 square units 8 square units 16 square units 3 y…

A: Area

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

A:

Q: For 1/2 U -dx and using the substitution -du -du 4u √4-(2u²) ² 4u du -du 1/2, the resulting integral…

A: In this question, we want to know the Integral form after substitution.

Q: x dx 7. The integral trigonometric substitution? sece tane de [s sece - 1 sino de S 1+ cose [sec²0…

A: We have to transform the integral using substution.

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

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Q: S For x 1/2 x-x3 dx and using the substitutionu=x1/2

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Q: QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: Please see the below picture for detailed solution.

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

A: To find the value of given integral.

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: Supposem and n are constants and m #n. Evaluate sin(mx) cos(nx) dx² 1 A -sin(m-n)x+ -sin(m+n)x +n)x]…

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Q: S²- 16-x2 A 2 B) 8 0 None 4 E dx is equal to

A: I am attaching image so that you understand each and every step. Option "C" is correct answer.

Q: 10. 3 J√cos z sin ³ zdz COS

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Q: ·S= x²-2x-In Evaluate 3x5 3x4+6x3-3x2 - 6x √(x − 1) 1/6(x+2) 16/3 (x+1) 1/2 (x-1) 1/6(x+2) 16/3 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: ·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)…

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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: Find the area bounded by the curve 4 square units O 16 square units O 8 square units 10 square units…

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Q: (cos-¹2w) 6. ¡ COS dw √1-4w²

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Q: consider ∫ xsinx cox dx= f(x) sin2x - g(x) cos2x + C. what is the value of f(1) + g(1)

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Q: Evaluate A B D Stan" tan" (x) sec4x dx. —tan (™+3)(x) + _____tan (™ + 1)(x) + C m+1 1 −tan (™+2)(x)…

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

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Q: If ["(x+5) dx = 14, then the value of b is equal to A) None B 2 C) 4 (D) -3 (E) 3

A: Let's find given integral.  We there is lower limit not given but it only possible 1.

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

A: Solved below.

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

A: To Find: Setup the integral for the force on one end of the trough.

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

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Q: Question 11 Evaluate: S₁ 2 A 63 16 B 105 C) None 16″ D 105 E 2π - 63 sinxcos³xdx is equal to

A: In given problem we solve definite integral using substitution method .

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

A:

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

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Q: 53 3-2x-x²

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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…

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