Use the method of substitution to calculate dx. + x² O a. In|æ|+C O b. In |1+x2| +C O c. arctan(x) + C Od. 글In|1 + z2| + C +C 2z+

Q: d (arccot(x)) -1 Be sure to provide a written justification for 5. Prove your work. dx 1+ x2

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Q: EVALUATE USING HALF-ANGLE SUBSTITUTION dx 5 + 4 sin a A. aretan (Stan (3=) + 4 arctan +C 3 В. 2 5…

A: This question is based on indefinite integral.

Q: 1 By using completing the square , dx can be rewritten as /x²-4x – 7 1 VTr- 2)²– 3 1 =dx V(r- 2)? +3…

A: We need to write the following integral by completing the square   ∫1x2-4x-7dx

Q: The suitable substitution to evaluate the integral /tan°(2x) dx is cos“(2x) O u= tan(2x) O u=…

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Q: Evaluate fl. 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

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Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 - y³)żdy

A: Given integral ∫b2y6-y812dy The objective is to evaluate the integral by trigonometric substitution.…

Q: Classify the ODE's according to their linearity. Write th solutions. (e cosxxy)dx 1 dy _ 1 ii) y4 dx…

A: Rearrange the ODE, 1y4dydx-1xy3=x by multiplying both sides by y4 and obtain dydx-yx=xy4. The…

Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.…

Q: +00 1 1 : dx x[In(mx)]3 m+3 8

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Q: Evaluate using the substitution u = 1 − x2 or trigonometric substitution.

A: Given: ∫x1-x2dx  ……1

Q: Specify the order and degree of the following ODE /2 d'y dy 1+ dx = y- dx2

A: Equation that gives the relation between variables and there derivatives is called differential…

Q: dx, Simpiny the dls ver using nyper ons. Select the corr oice. 2x 1 +C O None of these. 2+1 + C 2 O-…

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Q: The function def ined by y=Acos(In(x)) +Bsin(In(x)) d²y dy is the solution of the following DE: x²-…

A: True . i.e. the function defined by y=Acos(ln(x))+Bsin(ln(x)) is the solution of the differential…

Q: (3y³ – x³) dx = 3xy² dy; y(1) = 2

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Q: O prove that : (2) DO 2x e dx a e +b where a, b >o

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Q: 25 - x2 In dx , if we let u=V 25 – x2 , then udu = - xdx. A True B False

A: On solving this we will get

Q: Which of the following is not an improper? A B D Sªcot (x) dx © Sese(x C E S'tan (2) de dx csc (x)…

A: We know that an integral is called improper if one or both of the limits of integration are infinity…

Q: The tanh (2x) sech (2x) dx is equal to sech? (2x) sech (2x) -2*) O A. 1 +C 2(e2 +e 3 10 B. tanh6…

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Q: Which one is not equal to o V(x + 3)³ dx. lim, 100 E i=n-1 (음 + 3)3. O lima-00 1ri=n-1 Li-0 2i+1 +…

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Q: du k Ət u with ди (0, t) = 0, du (L, t) = 0, and u(x,0) = f(x). Əx²

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Q: Find an equatlon Of the ine Through G1,2); Perpendicular to me 2x+ 5yt 8=0 line

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Q: Complete the evaluation of V4 x make sure to express your answer in dx in Example 2; terms of x.

A: Consider the provided integral, ∫x24-x6dx Solve the above integral and write down the answer in term…

Q: S°1- (In x)2 dx=? If u= In x, then e A B L (1- u)du .2 © (1-u²)du

A: Given: I=∫ee21-lnx2xdx   ....1

Q: If y = tanh"( k /x) and vx (1 - 9x) y'=A Then A =... Answer:

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Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: Determine how large the number a has to be so that 1 dx Submit Answer

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Q: Given; √ √ tex dx 2 Applying rationalizing substitution, find dx in terms (A) z dz 2+z² 2 z dz B…

A: Given query is to find the dx in terms of dz.

Q: The sutiable substitution for evaluting | csc " (x)cot°(x)dx is (a) u = tanx (b)u = cotx (c) u =…

A: The given trigonometric equation is: ∫csc7(x) cot5(x) dx

Q: The suitable substitution to evaluate the integral tan (2x) dx is cos“(2x) none O u= csc(2x) O u=…

A: Given: ∫tan52xcos42xdx

Q: Solve the diferential eguation with discasfssic Of soaL (4xy-y2) dx +(2x? - 2 xy + 2y?) dy=o

A: Given the differential equation is 4xy-y2dx+2x2-2xy+2y2dy=0 This is form exact differential equation…

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1\ dy…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to x

Q: determine an expression for dyl dx a)y= 2x*+ e*+ 2x² tan(x)+TT

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Q: When applying substitution (u=tan(x)) to [s sec¹(x) tan(x) dx is equivalent O a) [ (u³ + u) du O b)…

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Q: Calculate dx and E at the points (1,649, 5) and (1,649, –5), where z is defined implicity by the…

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Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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Q: (a) Evaluate by solving the work for (i) Sxe-*dx.

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Q: 1 Using the fact that 1 du = -tan (-) +C, which of the following is equal to a² + u? 2x dx? o 16+x

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Q: Evaluate: Jx?cos(2x)dx 2x?sin(2x) + 2xcos(2x) – sin(2x) + C A 4 2x2sin(2x) + 2xcos(2x)+ sin(2x) (B +…

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Q: Suppose u = er sin (p), p= sin(3x), q = z² In(2y) , and r = ?. Assume that –7/6 < x < «/6. Compute…

A: Partial differentiation is termed as the differentiating function with respect to the single…

Q: dz is given by ди Let z= sinh -(y - 2x), where x = we e-3u and y= In then - OA. 6we -3u Vi- (y- 2x)?…

A: Here we will use chain rule of differentiation. and d/dx(sinh^(-1)(x)) =1/√(1+x^2)

Q: Ⓒ'Evaluate Sot So Sox sing ²sin y dy dz dx tim of the

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Q: (a) By using the substitution, u = 1+ x*, or otherwise, find x3 dx 1+ x*

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Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: dy +. (x>0) tind the Soiution of the difperential equation, expressing 4explicitly as general 4…

A: First we comparing the given differential equation with dy/dx+Py=Q .and then find I.F. and then…

Q: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

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Q: Step by step explanation how to solve this problem.

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