What is the derivative of the following? sin(t) d dt f 117 da cos(t) s(t) 4-sin² (t) 1 4 — sin² (t) cos(t) 4-sin² (t)

Q: 3x5 3x4+6x³3x² - 6x B с + + x + 1 x+m Consider S А Sx √x-m+A x-m+ 14/3 17/6 6 5 -dx. Using the…

A: solution

Q: To evaluate parts? A [x²cosx dx. use integration by parts. What is the expression after the second…

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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 B)…

A: Given that ∫x sinx cosx dx=fxsin2x-gxcos2x+C

Q: Question 8 x1/2 S dx and using the substitution = x 1/2, the resulting integral takes the form: X-X…

A:

Q: Estimate the slope of the tangent line to the curve at the given point (-0.5,4.998) on the graph to…

A: It is clearly seen in the figure that the tangent line is horizontal to the x axis at the point…

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

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Q: The integral [₁ face 8 dx S can be transformed to which of the following when trigonometric…

A: We have to solve above integral

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

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Q: Suppose m and n are constants and 1 1 —sin(m− n)x+ - -sin(m+n)x+C 2 m-n m+n 1 = cos(m− n)x - 1…

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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: 3 3--x2+3x and the line y=x. 4 Find the area bounded by the curve y=-x³- 16 10 square units 16…

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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: 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: ·S- y dy Vy+2 using the substitution (√√y+2-5) (5√√y+2+y+21) +C 0²/(√y+2-5) (5√y+2+y+24) + C ○ ¾…

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Q: Suppose m and n are constants and m #n- Evaluate [ sin(mx) cos(nx) dx -cos (m + n)x] + C 1…

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Q: dx (x²+4)² The integral A÷/csc²³ Ⓒ + /sec²0 B C Ⓒ + / sin² D 8 csc ³0 de c³0 de cos²0 de sin ²0 de…

A:

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

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Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

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Q: 1 3 Find the area bounded by the curve y== -x3. -x² + 3x and the line y=x. 16 10 square units 8…

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

A: To find out the bounded area by the curves.

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: What is the value of f(1) - 168 in x3 Inx dx = f(x) ((1/4) Inx - B) + C? 02 8 8 0 3 1

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

A: Solution of the problem as follows

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: ormulas to compute the following antiderivative. x-1 x² -dx.

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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: 3 Find the area bounded by the curve y= -x3x2+3x and the line y=x. 16 O 16 square units O 8 square…

A: Please follow the next step.

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: Question 9 The integral S x dx x²+√√x²-1-1 A /co B / Ⓒece s cose de 1 - sine sec²0 de 1+ tane secᎾ…

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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: The volume of a cube is growing at a rate of 225 ft3/min, and the length of a side is 5 ft. What is…

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

Q: What is the approximate value of 24 that is found using the tangent line to at x = 16? Round to the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider ! x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 3/8 1/2 0…

A: The objective is to find the correct option.

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 x dx x² + √x² can be transformed to which of the following using trigonometric…

A: ∫xx2+x2-1-1dx=∫secθ.secθtanθsec2θ+sec2-1-1dθ=∫sec2θtanθsec2θ-1+sec2-1dθ=∫sec2θtanθtan2θ+tanθdθ=∫sec2…

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: 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: For x 1/2 dx and using the substitution u=x1/2, the resulting integral takes the form: 4u -du 4-12…

A: We can solve the integral by using substitution .

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: y dy Find S- y+2 A ²/(√x+2-5)(-5√/y+2+y+21)+C ℗ ²/(√3+2-5) (5√/y+2-y+24) + C B Ⓒ(√x+2-5)…

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

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

A: Explained below

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: S x dx x²+√√x²-1-1 The integral substitution? (A) [sec²0d0 1+tan cose de (B) 1-sine sece tane de…

A: Simplify and substitute x = sec θ to get the answer.

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: QUESTION 6 ·S. sece tane de sece - 1 The integral cose de 1-sine sec²0 de 1+tano sine de 1+ cose x…

A: Let's transform given integral.

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

A: We have to find ∫sinln(x) dxWe will apply formula for integration by parts.We know, ∫uv dx…

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…