1. S(3 – t?)e6t-t*dt

Q: Find R f(x, y) dA where f(x, y) SIR f(x, y) dA- = x and R = [0, 4] × [-2, 4].

A: Given f(x, y) = x and R = [0, 4] x [-2, 4]

Q: b) (2 points) Find the exact value of the following integral. Show all your work. 1 5 + 2x + 3 4e" )…

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Q: The region bounded by the graph of y = x²VIn x and the x-axis on the interval [1, e] is revolved…

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Q: (cos v)³ + sin v dv (cos v)²

A: The given integral is: ∫cosv3+sinvcosv2dv Let I=∫cosv3+sinvcosv2dv

Q: S (x² – 12x + 100)(6 – x)dx -

A: We can solve as follows

Q: 1 x2 - 3x + 2 dx

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Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: ou provide the solution to get the integral after substi

A: Comparison Test for improper integralsIf  on the interval  thenIf  converges then   also…

Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

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Q: S 4x cos(2 – 3x) dx

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Q: Use the appropriate methods to solve the integralss in the picture below

A: We have to evaluate the given integrals.

Q: [17(xe" +e* )sin(xe*)-14sin(x)dx

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Q: =7 (1+ cos(t*)) dt. Find g'(z). COS x2

A: g'(x)=ddx(∫x26(1+cos(t3))dt) using fundamental theorem of calculus…

Q: |[Practice Problem] Solve and calculate the double integral by making a proper change of variables…

A: Let x+y=ux-y=v Then the enclosed region becomes Consider y=1-xy+x=1u=1 Consider y=xx-y=0v=0 Consider…

Q: (3+e2*-1)² dr

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Q: Why do we find the value of the integral without solving it?

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Q: y(t) +4 et"y(t – v)dv = 3. Let Y(s) denote the Laplace transform of y. (a) Apply the Laplace…

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Q: TT π So x² 2 √x²+4 dx

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Q: 6. Using Cauchy's Formula to evaluate 1 dz 2ri Je (4z – 1)(2 – 4)' 2ni being careful about factors…

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Q: 3sinx drIsSin3X dx ix

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Q: 00 Σ n=2 In n 2 n

A: Note:- As per the guidelines we are supposed to attempt only one question so please upload the next…

Q: = u(x) = x cosh x -√² - tu(t)dt

A: As per the question we are given a Volterra integral equation and we have to find its solution u(x)…

Q: 2. / 3" csc²(3") sin“(3") da (3") sin®(3") dx

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Q: 13 dt 9+6t 4 (9+6t)5

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Q: Evaluate S(e²-x²)(x) dx e2-x2 a) + c b) —е2-х? + c | e2-x2 c) -+ c d) e² – x² + c

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Q: co|= 5 Thus fff(x, y)dA = [' [ А 0 drdo

A: To determine the double integral shown below.∬fx, y dA=∫0π3∫15? dr dθAlso, to evaluate the above…

Q: Let f(x) = x for-4 sx<4. Because f is odd on [-4, 4), its Fourier cosine coefficients are all zero.…

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Q: 1. Evaluar la siguiente integral aplicando los Método de Gauss Legendre. [₁² (2x² + 3x + 5)dx 2.…

A: For polynomials of 2nd degree, we can use the 2−point rule.The Gauss-Legendre 2−point rule is given…

Q: So So So A² sin() ² sin (772)²sin()² dxdydz = 1, (A, a, b, c are all constants) b C Solve the…

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Q: سان (1-e dt 8

A: Given integral:- ∫0∞1-e2t2dt

Q: sin 1+V dz

A:

Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: 2 dydx -23-1 (xy)³ SS.

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Q: Let f (x) 1 and g(x) %D Find the area A of the region between the graphs of f and g on the interval…

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Q: [p'(8+3p*)®dp

A: Given: I=∫p78+3p48dp  ...1   The Power rule: ∫xndx=xn+1n+1+C

Q: Can you please solve this integral with a step by step explanation?

A: Step 1: Step 2: Step 3: Step 4: