dx √ 1 + x² Using three point Gaussian quadrature formula, evaluate

Q: Q4) Solve the D.E = *-**y²+2x* ya dx

A:

Q: exi solve the Disserentail equatione using homogenous method (x₁² + y) dx-xdy -o

A: given differential equation

Q: Find - 6x+1 x² +1 -dx.

A:

Q: Y-(92x²2x) (4x + 92x²) Find the dy

A: Product Rule of differentiation : du.vdx=udvdx+dudxv. dxndx=n.xn-1

Q: d A) show that: (x³) = 3x² . dx

A:

Q: dx Vx + a + Vx + b

A: Given: The integral is ∫xx+a+x+bdx

Q: | (3 + xx) dx

A:

Q: a va?-x? a²-x² (x + y) dydx

A: We have to find the value of given intregation.

Q: Y. 45° 45° 5.

A:

Q: Arctan°9x dx =b Arctan 3x+C, i+9x2 what is b?

A: Solving the given integral by substitution.

Q: Let: f : R → R with f(x) = 2x ^2 + 1. Prove or disprove that f is injective (one-to-one).

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Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: Use geometry to evaluate (2x + 6) dx. -5

A: We know definite integral   ∫abfxdx represent the algebric sum of the areas between x=a to b and…

Q: Evaluate /x* V5 - x*dx

A: We have to evaluate the integral: ∫x35-x2 dx Rewriting the integral, ∫x35-x2 dx=∫x2x5-x2 dx Now…

Q: Find sec 0. ? (7, V15)

A:

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: Q2\ Evaluate : fot√x dx

A: The given integral is ∫cot2xxdx use the identity  cosec2x-cot2x=1 cosec2x-1=cot2x therefore the…

Q: Find dx5 d³y for y = sinh(4x²) – /coth(6x³) %3D

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Q: Find the distance d between z1 = (8+ 8i) and z2 = (-8+ 8i).

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Q: dy Find if dx y = (3x2 + 6x – vx)(5x + + 10). DO NOT SIMPLIFY.

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Q: Ⓒ Differenitale y = √3x-7 X

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Q: dx Vx4 – 2x² + 1 3,

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Q: V3 3 9) 9 +x2

A: The given integral,        ∫0339+x2dx