What is the definite integral represented by the limit lim (+4) Ax, on the interval [-1,1]? n-x • /²₁ (2²+4)dz of, 2x dz of 2² de 0 1²₁ 1²² ²³ +4 2-3 +4x) dx

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

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

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Q: ·S- y dy Find using the substitution u +5=√√y+2. √√y+2 ²² (√y+2-5) (5√/y+2+y+24) + C (√√y+2-5)…

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Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 01 3 00 02

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

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

A: The region bounded by the given curves x2=4y & y2=4x is: which is rotated around y=4.

Q: Evaluate A B D Stan" (x) sec¹x dx. 1 (m+1 ¹) (x) + m+1 1 )(x) + m+3 2) (x) + m+2 -¹)(x) – m+1 tan…

A: We will evaluate the given integral by using substitution method as shown below

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

A: Given

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: Find S y dy Vy+2 D using the substitution u + 5 = √y+2. A √y+2−5) (5√√y+2+y+24) + C Ⓡ(√9+2-5)…

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Q: Exercises To Solve [N0.5] -2 05² = dx 2 x²+2x+5 5² 3dx 9x²-6x+5

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

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Q: Question 3 To evaluate A B D te fx-cost x²cosx dx use integration by parts. What is the expression…

A: The objective is to find the correct option.

Q: Exercises To Solve [No.5] 3dx 9x²6x+5

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

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: QUESTION 12 Evaluate Stan" (x) sec¹x dx 1 -tan (m + 1)(x) + m-1 -tan (m + 1)(x) - — ¹ m-1 -tan (m +…

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

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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…

A: Solution is here

Q: ·S- Find y dy Vy+2 using the substitutionu +5=√√y+2. A √y + 2 − 5 ) ( 5 √√y + 2 + y +24) + C (В…

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

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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: S sec²0 do 1+tano seco tane de seco - 1 The integral O 1: S S x dx x²+√√√x²-1-1 coso do 1-sino sino…

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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: What is the value of f(1) - 16B in ∫x^3 lnx dx= f(x) ( (1/4) lnx - B ) + C

A: To find out the required value.

Q: Given: 3z = xy_Find ƒ² + fy² +1 **+*+9 Option 1 Option 3 x²+y²+1 ²+²+3 9 Option 2 None of the…

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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: 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 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: Question 14 π 5ñ Find the area bounded by the trigonometric curves y = sinx and y=cosx from x = —to…

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Q: Consider ·S= x-m+- Sx 3x5 -dx. Using the method of partial fractions, the given integral can be…

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

A: Let's evaluate given integration.

Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B ) + C? O 0 01 2 со N 3 4

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

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

A: Here is the solution of the given problem. Method of Partial Decomposition

Q: Question 1 A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³).…

A: We need to find the integral for work done in pumping the content to a point 3m  from the top of…

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

A: This question can be solved using the concept of integration of trigonometric functions.

Q: dx The integral can be transformed to which of the following when trigonometric substitution is…

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Q: Evaluate tan" (x) sec¹x dx A B © D -tan (m+3)(x) + ¹ -tan (m+1)(x) + C m+3 m+1 −tan (m +1)(x) — —_¹…

A: This question can be solved using the concept of integration by substitution.

Q: Using the tangent line to the graph of the function f(x) = In(x2 + 1) at x = 2, what is an…

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