O 15.21 square units 33.43 square units O 43.23 square units O 22.89 square units

Q: 154. Use the Fundamental Theorem of Calculus, Part 1, to find sin x d dx √1-t²dt.

A: Topic = Derivative

Q: The volume of the solid generated by revolving the region bounded by x squared equals 4 y and y…

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Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

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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…

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Q: Question 12 What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? (A) 1 B) 3 2 D

A: Please see the below picture for detailed solution.

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

A: Option C is correct  4-x^2/4

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

A: Solution of the problem as follows

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

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Q: Question 10 The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x…

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

A: We have given integral  I = ∫x12x-x3 dx u=x12 du=12x12-1 dx du=12x-12 dx du=12x12 dx 2du=dxx12…

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: Question 8 dx The integral s can be transformed to which of the following when trigonometric…

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

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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: . Given u = (-3,-4, -1), v = (6,2, -3), find (a) ||u|| (b) ||u+v|| u (c) u + v (d) u+v

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Q: ·S- x² + sece tane de sece - 1 e integral sec²0 de 1+tan cose de 1-sin sine de S x dx can be…

A: We have to find the integral

Q: QUESTION 9 S x²-2x-In + In Evaluate 3x5 3x4+6x³-3x² - 6x O x2−2x 2 O x² - 4x O x² - 4x 2 て + In + In…

A: Solved below.

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: 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: [sin(mx) cos(nx) dx 9. Suppose m and n are constants and m #n. Evaluate 1 1 -cos(m− n)x+ -cos(m+n)x…

A: Evaluate the integral

Q: Suppose m and n are constants and m #n. Evaluate A B C D [sin(mx) cos(nx) dx. [„ _m cos(m − n)x -…

A: Here's the solution, please have a look at it..

Q: Question 4 Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the…

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Q: Evaluate sin(1 sin (Inx) dx Integration by parts will be used repeatedly. What is the expression…

A: The objective is to find the right option.

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

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Q: QUESTION 15 Evaluate sin(Inx) dx Integration by parts will be used repeatedly. What is the…

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Q: S- S- °S- S For x 1/2 x- U U 1-u4 4u dx and using the substitution -du -du -du 4u √4-(24²) 2 -du…

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

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

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

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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: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

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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: Find 1- y dy y+2 using the substitutionu +5= √√y+2.

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

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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: Evaluate 3x5 3x4+6x³3x² - 6x S₁ x²-2x-In x² - 4x 2 x²–2x 2 x² - 4x (x-1) 1/6(x+2) 16/3 (x+1) 1/2…

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

A: On solving this we will get Option (B) is correct

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ( (1/4) Inx - B) + C? A 3 (в 0 с 2 D 1

A: We have to find the value of f(1) -16B where it is given that  ∫x3lnxdx = f(x){(1/4)lnx - B }+C    @…

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

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

A: We have to find out value

Q: For the function y = (9x2 - 27)/x3 , determine the increasing and decreasing intervals, and identify…

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Q: S ' | Sc Sex²0 The integral dx (x²+4)² see c³0 de s²0 de csc ³0 de sin ²0 de can be transformed to…

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

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

A: Here is the solution of the given problem. We use here Washer Method

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

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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.