a) S In Gxt1) dx 2.

Q: Solve the following integral S,x²e*y dxdy

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Q: Solve the following integrals: a) SVI+ - v2 dx b) Sxcos 2x? dx

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Q: Solve the two items using Integration by parts. 1. (x' V9-x? dx

A: Question - 1:- Given: ∫x39-x2dx Formulas used: ddxxn=nxn-1ddxconstant=0ddxfgx=f'gx·g'x        Chain…

Q: ** Using the substitution y=x, the integral eln24 evx dx is the same as or equal to

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Calculate the given integral: S4 sec°(11x) dx

A: Given : ∫4sec611xdx

Q: Solve each of the following integrals using integration by part: a) 3x² In 2x dx b) [5xsin 3x dx

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Q: 1 Use the integration formula ax dx = ax + C to find 4* dx and simplify. In(

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Q: B) Use the techniques of integration to evaluate. (Solve 2 only) 3) J tan-ty dy dx 2) (1– x²)5

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Q: dx (b) J sin x· cos² x

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Q: Find the integration to de 0. a+bcos² 0

A: Given ∫02πdθa+bcos2θ. The given integrand is even function  We need to evaluate the above integral.…

Q: Given the integral 6e3x dx

A: The given integral ∫6e3xdx can be evaluated as,  Put, e3x=t 3e3xdx=dt   e3xdx=13dt Therefore,…

Q: Supply the missing integrand and the limits of integration - 2sin 0 r cos?0 dr d0 = _d®

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Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

Q: Use integration by parts to derive the following formula. In x 1 x. In xl dxx"+1 n 1 C, n1 (n+1)2

A: Assume u=ln|x| and v=x^n

Q: Evaluate the integral below using 2 point Gauss-quadrature and compare your results with the exact…

A: Given that, the integral is ∫15∫065y3+2x2+5dx dy. Note that, the formula for 2-point…

Q: xsin(x³) dxdy

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Q: Find the value of dx (7x – 2)° If the integral diverges, give "oo" as your answer. -

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Q: * = cos(x + y), when x = 0,y = %3D dx

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Q: The value of the double integral 45 dx dy is – 1890 1890 945 945 -

A: Given that ∫03∫0745dx     dy find out the value

Q: Find the integrals. Ax dx a)

A: Given : ∫5e-4xdx

Q: Evaluate the following by changing the order of integration: 5 sin(y*) dy dx. 5x

A: First we change the order of integration and find limit of integration.

Q: -x2 - 4x + 18 -dx J (3x + 4)(x2 + 9)

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Q: Solve the two items using Integration by parts. 1. [x' v9-x? dx Se sin x dx 2.

A: To find the given integral by integration by parts :-

Q: Which of the following uses integration by parts? (1) fxcos.x°dx (3) fxlnxdx (2) [x'e*dx - In x dx…

A: we have to find the integration by parts from the following

Q: Solve the following Integrals by Substitution 1 (a) dx 1— 4г2 et -d.x 1+ e2x (b

A: (a) To evaluate the integral: ∫11-4x2dx Solution: Let substitute t=2x. Differentiating both sides,…

Q: 2. 21-/9 – 4ª dx

A: The by parts method is given as ∫uv=u∫v-∫u'(v) where u is the first function and v is the second…

Q: dx 2x² 2. + 6

A: Given ∫4x2x2+6dx In order to solve the given integration first substitute 2x2+6=u and then proceed.…

Q: (b) Solve the following integral by using the Integration by Parts. e* cos 2x dx

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Q: x2 dx V(12 – 8)5

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Q: Use the appropriate technique of integration to solve the following. (a) In x? + 1dx

A: SOLUTION-

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: 6 sec*x dx

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Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

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Q: In using the technique of integration by parts, you must carefully choose which expression is u .…

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Q: Solve the following integral xe* dx 1

A: Calculate the integral         ∫12xex3 dx

Q: Solve the following integral by using the Tabular Method. (a) x² cos 4x dx (b) sin 3x cos 4x dx 2.

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Q: dx 3x2. dy ' y + 1 7(у + 1) 3 о

A: Let's find.

Q: Evaluate the following integral. dx 1+ e2x - In 13 ex dx = 2x 1+ - In 13 (Type an exact answer.)

A: ..............(1) take ................put it back in equation 1

Q: | -2" dxr. (x² + 1)e

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Q: find formulas for the functions represented by the integrals.

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Q: given 3 +3 dz where A J 2x+1 -2x²+X+) and B are integration. 2 and 1 Pespecti vely. Solve the

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Q: Solve the following integrals: i. S(e**sin(2x))dx using integration by parts or tabular meth

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Q: Consider evaluating x ln x dx using integration by parts. Which of the following would be the best…

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Q: Given that 1 dx = and x2 dx = , compute the integral. x dx = 4 2' 3' La - 20?. (1 – 2x)³ dx

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Q: 2) I = S t? sin ßt dt

A: Standard Formula that has been used are ∫sin(ax)dx=-cos(ax)a∫cos(ax)dx=sin(ax)a

Q: Solve the following Integral Equation: -t + x(0) = 3 %3D

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Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: sec{s)ds

A: We know, ∫abf(x) dx = ∫abf(a+b-x) dx

Q: х+1 dx 3 2 2 25 - x

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Q: Determine the following convolutions by integration (a) 1 * sin wt (b) et * e

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