Find the integration distance (f, g) = | f(x)g(x) dx between the given polynomials. f(x) = -5x + 1, g(x) = -2x + 5 d(f,g) = Ex: 1.23

Q: Find the integration distance (f, g) =| f(x)g(x) dx between the given polynomials. f(x) = -6x + 3,…

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

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Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: 7. Evaluate using integration by parts: f Væ log, x dx.

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Q: Find x" In x dx; n # -1, n real. (Use C for the constant of integration.)

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Q: a=1 and n-1. Let f(t) = tet SHOW all of your steps of integration clearly.

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Q: 2 3x 2. Evaluate f x'e* using integration by parts.

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Q: 3. Solve this third-order ODE by using the method of undetermined co- efficients: y" – y = exp x . -…

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Q: Determine an integrating factor and solve the followir xdy-ydx-(1-x')dx = o 1.

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Q: Find the integration inner product on C[-4, 2] of the given functions. f(x) = 20x g(x) = 3x3 %3|…

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Q: Show that 1, x, and x2 - ½ are orthogonal, when the integration is from x = -1 to x = 1. Write f (…

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Q: Find the simplest integrating factor u(x) of - xy' = (8x + 9)y + x In(x). µ(x) = %3D

A: As the given equation is an first order differential equation ,we can find integrating factor.

Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

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Q: 3. Reverse the order of integration in S(2xy + 1)dxdy and then evaluate.

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Q: (t² + 2t) dx = 2x + 8, x(1) = 1 dt

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: Find the integration distance (f, g) =| f(x)g(x) dx between the given polynomials. f(x) = 6x + 2,…

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

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Q: 89. Use the chain rule to prove the formula for integration by substitution: |f (u(x))u'(x) dx =…

A: To prove ∫f'ux u'xdx=fux+C by substitution. Solution: Let substitute t=ux. Differentiating both…

Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

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Q: Reverse the order of integration in the following integral. 7 14-2x !! f(x.y) dy dx y14-2 Reverse…

A: From the given integral; I=∫07∫014-2xfx,ydydx Now find the x-intercept and y-intercept.…

Q: 2 V4 – x²dx 0.

A: A detailed solution is given below

Q: Find the integrating factor: ydx+(3x-xy+2)dy=0

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Q: 2. Use the substitution u = x² and then Integration by Parts to evaluate / x³e**dx.

A: Given: ∫x3ex2 dx We substitute u=x2, that implies du=2x dx. By using this substitution, ∫x3ex2…

Q: Solve by finding an integrating factor which has non-exact ODE and also find integrating factor from…

A: The differential equation is given as (xy2+y)dx-xdy = 0                        (1) Let the…

Q: (b) Show that I(n + 1) = n · I'(n), using integration by parts.

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Q: Q3: Reduce the integral Sx³J2(x) dx to integration in terms of Jo(x)

A: To find - Reduce the integral ∫x3J2x dx to integration in terms of J0x.       Formula used - Bessel…

Q: cos(x + y), when x = 0,y = dx

A: To solve the given first order differential equation using integration method. dydx=cos(x+y)  , when…

Q: Consider the integration of f(x) = 1 + e* sin(4x) over the fixed interval [0, 1]. Apply composite…

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Q: Find the integration inner product on C[–4, 1] of the given functions. f(x) = 15x g(z) = 3r* (f, 9)…

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Q: x²-2x* 5. Integrate with respect to x x4

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Q: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

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Q: 6X By applying partial fraction me aod, find tne integration : S dx. X2+4x-5

A: We will find out the required value of given integral.

Q: Evaluate f x²+8x+15 dx by using the integration by partial fraction.

A: We will factorize the denominator and then separate hose factors by using partial fraction method.…

Q: exact method: (3xy3 + 4y)dx + (3x2y2 + 2x)dy = 0

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Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

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Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: 5. The integration form of , XY dA where Dis the portion of x+Y = 2 in the 1" quadrant will be

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Q: Find the integration of (1+ 2x)dx using Trapezoidal and Simpson's Rules for n=6

A: Given integral  ∫061+2xdx The Trapezoidal rule states that…

Q: Which of the following can be evaluated directly by the Power Formula of Integration? Sx³ V25 – x4…

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Q: 3. Show that the DE is not exact, determine the integrating factor, make it exact and solve. a. (2y…

A: The given differential equation is…

Q: 2. Reverse the order of integration and then evaluate. So S, x² sin(xy)dxdy а.

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Q: Find the total differential of z = In (2x – 3y).

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Q: 1 dy 3 yz-+ y7 = 1, when x = 0, y = 3 dx

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Q: X+3 Q4) Find the integration by using: J: dx 2x3-8X

A: This question is based on indefinite integral.

Q: Given f (x) = x – z² + 1 %3D - defined over the interval [0, 6]. Use integration methods to solve

A: (a) The interval [1.5, 5] is divided into 8 points, so the 8 points are (1.5, f(1.5), (2, f(2)),…

Q: Find the integration inner product on C[-3,3] of the given functions. f(x) = 16x g(x) = 3x² (f, g)…

A: Explanation of the answer is as follows

Q: Show that if an integration formula of the type I„(f) =£w;f(x;) j=1 is exact for 1, x, x², ...x",…

A: According to question given:Inf≈∑j=1nwjf(xj)Is exact for 1, x, x2, ...xm for a natural number m.We…

Q: Determine the first three nonzero terms in the Taylor Polynomial approximation for y' = cos x + e2x,…

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.