Integrate each of the following. Show complete solution. 1. 1000dx 2. S²x¹ + 3x² + 1)dx 3. f(u² + u + 1)du 4. (v¹ + v² = v) dx

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: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

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…

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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…

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Q: Question 14 Find the area bounded by the curve y = - -x 16 A 10 square units B) 4 square units C 8…

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Q: What is the of y = (tan-¹4x)² ? 2 - 2tan ¹4 1+16x² 1 8tan ¹4x 1+16x² 2tan-1 ¹4x 1+16x² -1 8tan ¹4x…

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Q: For the function y=x√ find the values of x for which the rate of change of y with respect to x is 6?…

A: Given: y=xx ⇒y = x32 Rate of change of y with respect to x is defined as dydx

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

A: Volume of revolution

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: 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: 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: 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: 4. f ta tan x sin xdx

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Q: π 5ñ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x== to x== 4 (A) 1.414…

A: Here is the solution

Q: 2. Given u = 8i - j + 3k and v = 7j - 4k, compute each of the following. (a) -3v (b) 12u + v (c) ||…

A: In this question, we have given two vectors u and v. We want to compute the given expression.

Q: 16. S cot xdx /1 + In sin x

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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: Evaluate Stan" (x) sec¹x dx- 1 A -tan ₂ (m+3)(x) + —_—_—_tan (m+1)(x) + C m+3 m+1 1 1 B −tan…

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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…

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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 volume of a cube can be represented using the function V(s) = s³ Which formula of the sphere is…

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

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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: 10. 2 x² +8 X + 2 אן dx

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Q: Exercises To Solve 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: 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: Question 16 Л 5л Find the area bounded by the trigonometric curves y = sinx and y=cosx from x=- to…

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Q: Evaluate Stan" (x) sec¹x dx. 1 -tan (+2)(x) +-tan" (x) + C m+2 m 1 1 -tan (+1)(x) + -tan (™-1)(x) +…

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

A: This question can be solved using the concept of area bounded by two curves.

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

A: topic - integration by parts

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: 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: 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: Evaluate Stan" (x) sec¹x dx. 1 A 1 -tan (m+3)(x) + m+3 m+1 1 tan (+2)(x) +-tan" (x) + C m+2 m 1 tan…

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

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Q: O 15.21 square units 33.43 square units O 43.23 square units O 22.89 square units

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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: 18. f(tan 2x + cot 2x)² dx

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Q: QUESTION 3 To evaluate x²cosx dx' x’sinx+2x cost – 2 x’sinx − 2x cosx+2 x’sinx – 2x cosx – 2 x’sinx…

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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: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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

A: We can rewrite the given integral by using this substitution u = x1/2

Q: QUESTION 4 To evaluate x²cosx dx' use integration by parts. What is the expression after the second…

A: The given integral is: I=∫x2cosxdx   Apply the integration by parts to solve the above integral.…

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

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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: Exercises To Solve [No.5] 6 "Cosx dx. Sin²x+25inx+5

A: Here is the solution