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Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: 1 5. sec y tan y

A: Given function is: f(y)=1secy tany Rewriting the given function: f(y)=cos2ysiny Find the integral of…

Q: sV2x - x'dx 2x – x'dx

A: We use appropriate substitution to compute the given integration.

Q: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: Find the most general antiderivative. show all work Integral (secx/secx-cosx) dx

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Q: Can you help step by step please?

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Q: find the derivativa dy for the frurrtion y=x by using lagarithmic differatiation.

A: Given y=x5x Taking logarithmic both sides, lny=lnx5x implies lny=5xlnx

Q: x*+6x° -dx x(x*+4)*

A: It is known that: ∫1xdx=lnx+C∫xndx=xn+1n+1+C Here, C is the integration constant.

Q: When using a change of variables u = g(x) to evaluate the definiteintegral, how are the limits of…

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Q: To integrate y3xdx we apply integration by parts and in the form u dv, u is set as:

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Q: Find the particular antiderivative that satisfies the following conditions:…

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Q: Use appropriate technique of integration to compute the antiderivative

A: Put,

Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: What is an antiderivative of **+2, x2+1 .. x + arctan x-5 2x +3 x + arccot x x + 2arctan x +1 A. D.

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Q: Use u-substitution to evaluate the integral. 3 + 5 Vx dx 3 2 + 5 Vx dx =O

A: Given query is to eveluate the integral.

Q: Ue fe Einemial Theorem to ine tre coeficit ofnthe eparsion of ir+ 31

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Q: x° 16x6 -24x3 +9 dx

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Q: a" cos xdx

A: the given integral is: we have to evaluate the given integral

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: 1. x° In x dx

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Given xdy-ydx=4x4dx

Q: Ernlate The following Improper integrok dx 2 (3 X2

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: What is the antiderivative of  (2 + x^2)/x^3 ?

A: Given information:The given function is

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, u is set as: Ox

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Q: Sx Arctan(x) dx

A: To find:              ∫ x tan-1x dx

Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 s y s 2, y – 1sx s 1} 328 3.

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Q: хIn x dx х Arctan (x) dx

A: The given integral is ∫x9 ln x dx Note:     Multiple questions are given, we are answer only one…

Q: Use integration by parts to evaluate  ∫x cos x dx with u = x and dv = cos x dx.

A: Integration by parts: I=∫xcosx dxFormula:   ∫uvdx=u∫vdx-∫[ddx(u).∫vdx]dxHere u=x , v=cosx

Q: To evaluate S (In x)² -dx, apply integration by parts twice. For the second application of…

A: Follow the procedure given below.

Q: Evaluate triple integral , S S dz dy dx. 4-y -2 Jx2 Jo

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Q: | 2°+Idal Vx² +1 dxl

A: The given integral is- ∫x3x2+1dx Let x2+1=u Differentiate w.r.t. x to both sides- 2x=dudxdu2=xdx…

Q: Use (a) the Trapezoidal Rule integral 1to 4    sin x dx                 with n= 5

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Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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Q: J (5x* – 10x + 12) dx

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Q: What is the antiderivative of the integrand dx ? 2e*

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Q: Use the appropriate technique of integration to compute the following antiderivatives. Show complete…

A: The given integral is: I=∫2x-x2 dx

Q: a) dz, T: z (t) = -e-int, 0<t <1. %3D -1 1

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the iterated integral. 3 (2z fIn(x) '3 xe-Y dy dx dz Jo

A: ∫13∫02z∫0ln(x)x e-y dy dx dz

Q: 1 sin? y cos? y

A: The antiderivative is the reverse process of differentiation. The antiderivative is also called the…

Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: x – 2 dx 9. J x² (x – 1)²

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Q: Evaluate the iterated integral. 3 4ze dy dx dz

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Q: ( b). Je2cos (πx) dx .

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Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

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Q: FCx) is continoos on L3,5) and S Fex) dx= 5 Evaluate integral

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: (a) In(4x) dx

A: Integration by parts:  ∫f(x)g′(x)dx = f(x)g(x) −∫f′(x)g(x)dx

Q: Change the order of integration 2 rIn(r)+1 f(r,y) dy dx Ji Ji

A: