iven that a and b are positive constants with a < b. how how you find the antiderivative and use the Fundamental Theorem to evaluate ti -b 2 In(x²) dx a

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A: Using residues, we have to evaluate the integralintegrate

Q: b. Stos-¹0 ¹(y) sinx √1+ sin2x dx dy

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Q: dz. 2ª + 9 tegrate

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Q: 7 I √49-x² 49-x²-z² Ľ -V 49-x² 1 √49−x²−z² (x² + y² + z²)¹/2 dy dz dx =

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Q: sin(2t +) dt = 64 7.

A: Note the formula for the integration by parts : ∫utvtdt=ut∫vtdt-∫dudt∫vtdt .

Q: Show that cos A x e 2 *,x2 0. %3D

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Q: cos x 4. Compute the integral 1+(sin x)? Hint: u-substitution

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Q: 1 |Using u-substitution we find that In(2x + 1) dx In?(3) 2x + 1 JO

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Q: Si dx using Part 1 of the Fundamental Theorem of Calculus. x4 Enter the exact answer. Evaluate the…

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Q: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

A: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

Q: dx √₁²x²+² x²+2x+10 dx using Gauss-Legendre and Gauss-Chebyshev Quadrature formulae. 6. a) Evaluate…

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Q: 25 The second degree Taylor polynomial for 5r -9 centered at ar = 2 is 1+ (a - 2) –( - 2)*.

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Q: sin 2ydy 5.J7-3 cos 2y 15.

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Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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