Find the cross product a x b. a = (7, 6, -5), b = (2, -1, 1) Verify that it is orthogonal to both a and b. (a x b). a = (a x b). b =

Q: What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx-B) + C? 02 0

A: Correct answer is 0.

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: Exercises To Solve [No.5] Lim 9-5 -4 dx 8X-15 "Cosx dx. 6 Sin²x+25inx +5

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Q: Find the area bounded by the curve y = 1x³ - 2x² + 3x and the line x3_ 16 16 square units 10 square…

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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…

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Q: [x²cos x²cosx dx, use integration by parts. What is the expression after the second integration by…

A: We will use integration by parts to solve this question.

Q: Question 18 Find - y dy (y + 2 A(√y+2-5) (5√/y+2+y+24)+C А Ⓡ(√y+2-5)(-5√/y+2+y+21)+C B Ⓒ(√3+2-5)…

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

A: The region is bounded by y=116x3-34x2+3x and the line y=x.

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

A: Follow the procedure given below.

Q: Question 19 5x Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=-to x=-…

A: Given

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

A: Given

Q: The volume of the solid generated by revolving the region bounded by x²=4y and is to be solved using…

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Q: 18. f(tan 2x + cot 2x)² dx

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Q: 3x³ -dx. Using the method of partial fractions, the given integral can be written as 3x4+6x3 3x2 -…

A: Here, 3x53x4+6x3-3x2-6x=3x53x(x3+2x2-x-2)=x4(x-1)(x+1)(x+2)=x-2+5x2-4(x-1)(x+1)(x+2)

Q: What is the definite integral represented by the limit lim (+4) Ax, on the interval [-1,1]? n-x •…

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Q: Evaluate A B Ⓒ D S= x² - 4x 2 x² - 4x 2 x2-2x 2 x²-2x-In 3x5 3x4+6x³3x² - 6x - (x-1) 1/6(x+2) 16/3…

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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: An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per…

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Q: 3. f(e-²x - 1) dx

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

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

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by , the x-axis, and…

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

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Q: pose m and n are const (-)+(+)x] + C m-n m+n [-cos(m-nx- -cos(m-n)x - cos(m + n)x] + C 1 m+n…

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Q: 7. fex tan¹(ex dx

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Q: 6 Ⓒh'(x) = 7(7x³+4x) (21x² + 4)

A:

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: 1/2 S x²√1-x²dx. 0

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Q: Evaluate tan" (x) sec4x dx. 1 1 (A) =tan(+3)(x) + _____tan ( + 1)(x) + C m+3 m+1 1 B) (m+3 -tan…

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Q: Question 15 Find the area bounded by the curve y = -x 16 A 8 square units B 16 square units C10…

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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: QUESTION 8 The integral O S fec S S O O ·S- O x dx x²+√√√x²-1-1 sine de 1+ cose sec²0 de 1+tane cose…

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

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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: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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

A: Integration

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: To evaluate x²cosx dx' x2sinx – 2x cosx+2 x2sinx – 2x cost – 2 x2sinx+2x cost – 2 x2sinx+2x cosx – 2…

A:

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

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

A: Integration by Trigonometric substitution.

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

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) 1/2 B)…

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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: 8. 5 cos²x - 3tan x COS X dx

A: