18 dx Integrate using trig. Substitution: S- x² V9– x²

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

Q: b) Change the order of integration for . S(x- Jy=o Jx3xy) dxdy then evaluate it. |

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Q: (2y – 3x)dx +xdy = 0 %3D

A: Find your answer below

Q: Cosx b) Jo esinx) x+1 dx, using the substitution u = sinx. 13. Find a) J1(x+1) e), (x + 1)e *dx.

A: In the question it is asked to solve question number 13.

Q: sec 2x da 4. I+3 tanzx

A: Integration methods help to find the answer to the problem. Substitution of the function helps to…

Q: 1. S(3 – 2x – x*) dx

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Q: Bx*e²*dx Integrate. J3x*e*rd

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Q: Evaluute the integra dx 0 16+49x2

A: Here we have to evaluate I=∫-∞∞dx16+4x2

Q: Evaluate using Integration by Parts. -8x sin x dx + C

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Q: dxdy Vy X'

A: Given: ∫01∫yy21y2-x2dxdy

Q: Mesin(2x) dx = e$in(2X) + C then the M is equal to Blank 1 If

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Q: xy(y? + 1)dx + (x²y² – 2)dy = 0, y(1) = 1

A: Given: xyy2+1dx+x2y2-2dy=0, y1=1 ⇒xy3dx+xydx+x2y2dy-2dy=0 ⇒xy2ydx+xdy+xydx-2dy=0 ⇒xy2 dxy+xydx-2dy=0

Q: S e6m sin m dm Integration by Parts

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Q: y Sin (x) dx dy -2 2.

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Q: Integrate the function. 8 dx V36 - 64x2 X+ C sin-1 + C -1 + C D 4 tan-1 3. B

A: Given:       ∫836-64x2dx  substitute u=4x3→dudx=43                   dx=34du         =∫636-36u2du…

Q: -2* dx

A: To integrate using tabular form.

Q: Find I using integration or geometry: I = 5 dx dy .

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: QA1 (a) Given that y = (3+4x²)° +10sin(5x) determine dx dy

A: The solution is given below  Please post separately

Q: Use the change of variables u3 = x2 - 1 toevaluate the integral

A: Given: I=∫13xx2-13dx                       ..1 for evaluating given integral we substitute x2-1=u3…

Q: 2. Integrate: Integration by Parts cos?x dx

A: Given : Integral cos2(x) dx

Q: 7) | dx (hint: use integration by substitution.) x' +1

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Q: 2) Integrate using trigonometric substitution (a) s dx 4- x² (b) S, dx Vx2- 9

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Q: 1 I = dx V(a-a)(x-a-2b)

A: Given data: The given integral is I=∫1a-xx-a-2bdx. The given integral can be written as,…

Q: Q1/ Evaluate the integral: -За (2уах 3a dy dx x2 4a by changing the order of integration.

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Q: Integration by Parts (IBP) 1. Sx³e*/2dx 7/4 2. SR" x sin 2x dx

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Q: To integrate 3x² e4² ΟΧ dx' we apply integration by parts and in the form u dv, u is set as:

A: ∫x3ex2dxTo do integration by parts we have to get it in the form ∫fg'

Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: 44. sin(V#) dr First make a substitution, then use integration by parts.

A: At first we make a substitute and then calculate the value of integration by 'By Parts' method.

Q: dx? dx dt + 5- + 6x = 4t2, where x(0) = 0,x'(0) 0 dt

A: Second order intial value problem

Q: b) y = [ dx Integrate. 13 +5

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Q: Jx cos 3x dx Using Integration by parts, what should be the u and the dv? O u = xdx, dy = cos 3x Ou=…

A: Given : ∫xcos3xdx    To Find : Value of u and v in integration by-parts

Q: c) Calculate the integration Y+1 dydx

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Q: Q3) Evaluate triple integral Lyx -y)dz dy dx.

A: Topic = Integration

Q: Q3) Evaluate triple integral (x2-y?)dz dy dx.

A: Introduction: When the integrand is a function of three independent variables, we use triple…

Q: dx 62 + x² Integrate:

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Q: [[ dx dy Q4 )Evaluate by changing the order of integration

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Q: 8 dx Q1 Evaluate | (1+ by trigonometric substitution integration method?

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Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .

Q: 2-r Change the order of integration and hence evaluate dy dx 2 + y?

A: To solve this problem. first find the region of integration by drawing the region and then change…

Q: M3.1 Integration by Parts (IBP) 1. Sx³e*/2dx S* x sin 2x dx 2.

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Q: b) Change the order of integration for So Sx - y) dxdy then evaluate it.

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Q: sinx dx 5+ cor?x

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Q: Integrate dy (a) y'Jy? +16 6. (b) V6x Vox-x* dx –

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Evaluate the integral. cost dt sin n² t - 5 sin t + 4 Select one:

A: We will substitute sint=x, then we will do partial fraction.

Q: Evaluate∫x3√4−x2dx using (a) integration by parts (b) au-substitution (c) a trigonometric…

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Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

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Q: 10 cos(x) Evaluate the improper integral: / dx Vsin(x) а) 30 b) O20 40 c) 3 d) Odiverges e) 10

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Q: The integration A. 114 Β. π C. 0 D. 1/2 Z|7 sinc(4nt) dt has the value (hint:use the FT)

A: Given integral is ∫−∞∞sinc4πtdt. We have to evaluate the given integral. Here, ft=sinc4πt. Now, for…

Q: 3 3 У(х'у + 2х — у)dx + x (ху — 2) dy 3D 0 3

A: Firstly we find Integrating factor, then find general solution.