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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: 3x5 3x4+6x33x2 - 6x + In Evaluate S Ox²–2x (x-1) 1/6(x+2) 16/3 (x+1) 1/2 2 Ox²-4x (x-1) 1/6(x+2)…

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Q: 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

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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…

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

A: To Find:Set up the integral for the work done in pumping the content to a point 3m from the top of…

Q: 17. Evaluate A. B. C. C 3x4+6x³3x² - 6x x² - 4x 2 x²-2x 2 x² - 4x + In 2 x²-2x-In + In -dx, using…

A: We have to calculate the given indefinite integral according to the given information

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

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

A:

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) 1/2…

A: We have to find the 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: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

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Q: QUESTION 18 The volume of the solid generated by revolving the region bounded by x2=4y and y2-4x…

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

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Q: x² - 16 to fill in the table: - 4 5 4.5 4.1 4.01 Based on ONLY the table of values above, what…

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Q: 53 3-2x-x²

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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 that A trough filled with liquid and                                 density of liquid =ρ =…

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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Q: y dy Find ·S- using the substitution +5=√√y+2· Vy+2 ²(√y+2−5)(5√/y+2+y+21)+C 3…

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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.

Q: Question 3 Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is 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 to…

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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: 2. f(x²+2x-3)(x+1)dx

A: We can find the integration as below.

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

A: Follow the procedure given below.

Q: QUESTION 16 The volume of the solid generated by revolving the region bounded by x²=4y and y2-4x…

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Q: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

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Q: The rate of growth of a population after t years is given by the equation P(t) = 5t. What is the net…

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

A: Vector

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

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

A: Follow the procedure given below.

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

A:

Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

A:

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

A: topic- area bounded by curves

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: ·S. The integral of sect S S x dx x²+√√√x². sece tane de sece - 1 sec²0 do 1+tano cose de 1-sine…

A: Given Problem:-

Q: dx 2. The integral S can be transformed to which of the following when trigonometric (x²+4)²…

A: Please see the answer below

Q: sin ydy (4 + cos y)²/3

A: We know that integration of xn is xn+1/n+1 +C. Here C is integral cosntant.       Here i attached…

Q: What is the definite integral on the interval [1,3] given by n lim n-∞ €k cos πæk Δα? 3 of x cos x…

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

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

A: Follow the procedure given below.

Q: What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx-B) + C? 0 2 0 3 01

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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: y dy Find ·S= √y+2 0²/(√y+2-5)(-5√/y+2+y+21)+C 3 03 (√y+2-3) (5√/y+2+y+24) +C 3…

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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: Washer Method

Q: For x1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: 4u -du -du…

A: topic- indefinite inegral

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: