Fined the specitic integrals (show calcoladion e x' (Inx) dx 1. /2 2) 7 sinx cosx dx 10 3) メ-MS 2. Ax 1-x 1)

Q: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 9x…

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Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx

A: The given function is continuous on the interval [0, 1], then using Simpson’s rule to find the…

Q: We have determined that du = 5x* dx. However, the given indefinite integral dx does not conta %3D x…

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Q: This enables us to use this equation to express the double integral as an iterated integral in the…

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: 14 Find the integrals using integration by parts. a. fx(x + 4) dx c. fx'e"dx e flnx'dx d. [(In x)°…

A: (g) The given integral is, I=∫lnxxdx Rewrite as, I=∫xlnxdx Here, ∫udv=uv-∫vduu=lnx and du=1xdxdv=xdx…

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. [x x cos…

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Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

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Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 7x…

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Q: Evaluate the double integral : (x + 2y – 4) dy dr

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Q: 2 sinh x Calculate the integral, J dx. 5+ 6 cosh x

A: Given :∫2sinhx5+6coshxdx

Q: 6) dx X 3 Type 2 mproper integral 1-

A: We use Type II improper integral  Here at x=0 f(x) is discontinuous so we break the limit at x=0 If…

Q: 20 Evaluate the integral dx dy by reversing the 0. 4. order of integration. NOTE: Enter the exact…

A: We have to find

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

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Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

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Q: Evaluate the double integral ∫0 to 1 ∫0 to x sin(y^2 ) dy dx by reversing the order of…

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Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: 3. (x²+x+4) dx

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Q: How do I calculate the indefinate integral of e^sinx(cos(x))dx

A: Given integral is ∫esinxcosxdx

Q: In the integration of (cos y)^2 dy/(1- sin y), what is the first step to solve the integral? *

A: Given,          ∫cosy2dy1-siny

Q: aluate the Cauchy principal value of the given improper integral. dx (x² + 1)²(x² + 9)

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Q: Identify an analytic anomaly why numerical integration formulas will fail for J_11-x² sin(ax) dx.…

A: Given integral is∫-11sinπx1-x2dx

Q: Evaluate the integral (8x +12y)dx + (9x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A: Topic:- integration

Q: 3. Evaluate the integral 3 dx dy by reversing the order of integration.

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Q: Consider the improper integral: x² +2x+2 dx what will be the appropriate solution and answer? A Im…

A: ∫0∞1x2+2x+2dx

Q: 1 Evaluate the double integral by reversing the order of integration 3* sin(xy?) dydx

A: First, we will change the order of integration then we will solve it.

Q: Evaluate the integral / (8x + 3y)dx + (18x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: Explanation of the solution is given below....

Q: Exatuate the integral pvz O√3 √4-X² √EX 9 (√x ² + y² dy dx

A: Evaluation of double integral by conversion to polar coordinates.

Q: Evaluate the integral (8 (8x+15y)dx + (27x - y)dy along the parabolic arc y = x² from (0,0) to…

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Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: 4 | a sin(3y+ x²)dydx, 2 a) Sketch the domain of integration on an (x,y)-plane. b) Set up the…

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Q: If the substitution x = sin y is made in the integrand of . - A dx, the resulting 1-x integral is

A: Put value in  given  integral

Q: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: Suppose we perform the substitution u=1+Vx in the integral dx . (1+Vx)5 What is the resulting…

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Q: Evaluate the iterated integral. (2х — 4у) dy dx Exact number, no tolerance. (2x – 4y) dy dx = i -1

A: The given integral is: I=∫111∫-11(2x-4y) dy dx

Q: By using Beta function and assuming x2 = y, the integral %3D -1/2 dx is equal to

A: Substitute x1/2=y or x=y2:  ∫011-x1/2-1/2dx=∫011-y2/2-1/2dy2…

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: 0.5 cos x In(3 sin x)dx = COS I %3D 0.1

A: Definition used -   U substitution - When there is a composite function multiplied by the…

Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: I+tgX dx; 2 COS X cos

A: Given: ∫1+tanxcos2xdx

Q: -sin20 B)Evaluate the integrals: i) f/2 sinze rdrde, 0 ii) f/2/2 finx 2² siny dz dy dx. 0 0

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Q: Evaluate the integral / (8x + 18y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A: We have to find value of given Integral along given Curve.

Q: Roro is looking at the iterated integral (x² + y²) dx dy and suggest to Mpho that the integral does…

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Q: 7. Find the indefinite integral. 1. dx V9-16x? 4x 1 tar arcsin 3 +C_b. arcsin(9x) +C a. 4 4x c.…

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Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows