Consider and C. -dx Using the method of partial fractions, the given integral can be written as 3x4+6x³-3x² - 6x x-m+ -+ + x-1 x+1 x+m dx- Find the sum of A, B,

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

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Q: y dy Find ·S= √y+2 0²/(√y+2-5)(-5√/y+2+y+21)+C 3 03 (√y+2-3) (5√/y+2+y+24) +C 3…

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Q: What is the value of 1)- 168 in x² Inx dir = f(x) ( (1/4) Inx-8) + C? 03

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Q: Suppose m and n are constants and m‡n- Evaluate sin(mx) cos(nx) dx* 1 1 2n-m 1 -cos(m-n)x- +COS (m…

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

A: The objective is to find the right option.

Q: Consider √(x-m. 3x5 -dx. Using the method of partial fractions, the given integral can be written as…

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Q: (C) Find dx (i) y= for the following functions : 3x 2x-1 2x+1 (ii) y=sec(sec ¹5x)+e5lmx +4

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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: 3x5 3x4+6x³-3x² - 6x B с -+ x-1 x+1 x+m S= Consider Sx-m+- A xm+-+- -dx. Using the method of partial…

A: Since the degree of the numerator is not less than degree of the denominator, perform polynomial…

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

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

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

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Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

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

A: The full solution of the question is given below:

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

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

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Q: waluate Stan" (x) sec¹x de m 1 m+3 −tan (m+3)(x) + 1 m+2 1 m+1 1 m+1 1 m+1 tan n (m+2)(x) + — tan”…

A: We will evaluate the given integral as shown below

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

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

A: solution

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

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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: 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: The integral I com S f se fse x dx x² + √√√x²-1. cose de 1-sin sinᎾ dᎾ 1+ cose sec²0 de 1+ tane sece…

A: Substitute x= secθ and solve . dsecθdθ = sec(θ) tan(θ).

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

A: Explained below

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: Suppose that f(x) = 24-223+2-3. Starting with 1 = 2 and using Newton's method, what is the second…

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

A: Solution is here

Q: aluate A B Ⓒ D Stan™ tan" (x) sec¹x dx. 1 M+2 - 777 +1 - tan tan (m + 1)(x) + tan (m + 1)(x) -tan…

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Q: The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is…

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Q: Evaluate tan tan" (x) sec¹x dx O 1 −tan (™+2)(x) + — tan” (x) + C m+2 m O 1 1 -tan (m + 1)(x) — — ¹…

A: To evaluate the integral

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: The table below shows the average rates of change for points near In (2) for the function f(x) = e +…

A: We have to find the instantaneous rate of change

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

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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: ·S= cost cose de . 1-sino sece tane de sec-1 The integral sine de 1+ cose sec²0 de 1+tano x dx can…

A: Let's transform integral by using trigonometric substitution.

Q: (B) Find equations of the tangent and the normal lines to the curve y-exy = sinh x² +ln(x+√y point…

A: Given the curve y-exy=sinhx2+lnx+y at the point P0,1

Q: Estimate the slope (slope rise/run) of the tangent line to the curve. N 3 4 6 N D-

A: topic- slope of a line

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: What is the value of f(1) - 16B in ∫ x3 lnx dx = f(x) ( (1/4) lnx - B ) + C?

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Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

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Q: For f x 1/2 dx and using the substitution=x1/2, the resulting integral takes the form: -du 411…

A: We know that integration of xn is nxn-1.   Here i attached the solution of this question.

Q: dx 3-2x-x² L

A: According to our guidelines we can answer only one question. Other questions can be reposted.

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: solve the DE b

A: The DE is (x-y+2)dx-dy=0or, (x-y+2)dx=dyor,dydx=x-y+2

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: 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: 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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