### Evaluate: Integration using Trigonometric Substitution

Please evaluate the following integral using trigonometric substitution. Please show all steps in the solution. Thank you. Integral sqrt(y^2 - 25) dy/y^3 y > 5.

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Please evaluate the following integral using trigonometric substitution. Please show all steps in the solution. Thank you. Integral sqrt(y^2 - 25) dy/y^3 y > 5.

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(See attached file for full problem description) Please follow instructions and show every last step please!

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(See attached file for full problem description)

Rewrite the integral to match it to a standard formula, and then solve the integral. ∫x²/(x² + 1) dx

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For laminar flow in the entrance of to a pipe, as shown in figure, the entrance is uniform u=U0, and the flow downstream is parabolic in profileu(r)=C(r0^2-r^2). Using integrla relations, show that the viscous drag exerted on the pipe walls between 0 and x is... Prescribed text book: White, FM, , Viscous Fluid Flow, 2nd Editi

Please evaluate the following integral using trigonometric substitution. Consider: Integral (9-w^2)dw/ w^2

Please help me evaluate the following integral using trigonometric substitution. Please show all steps involved. thank you. The problem is: ∫3dy/ √(1 + 9y²)

See attached file for full problem description.

Can you please provide a detailed explanation of how to evaluate these questions? (See attached file for full problem description)

Question 1: What is the exact value of ∫ 0-->2 x^3 + 3x^2 dx ? Question 2: Find SIMP(n) for n = 2, 4, 100. What is noticeable? ---

Please see the attachment for the questions.

Please evaluate the following integral using the formula for integration by parts, int (udv) = uv - int (vdu) Int z(ln z)²dz

Please evaluate the following integral using the formula for integration by parts, ∫udv = uv - ∫vdu ∫e^(-2x) sin2xdx Please show detailed solution, including substitution(s) used.

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Using the formula for the length of a curve y=f(x) from a to b L=∫√(1 + (dy/dx)²)dx Find the length of the curve: y=x³′² from x=0 to x=4

The area I am looking for is the region bounded by the two functions y=x² and y=2-x between the limits (2,0) and (0,0) and bounded by the x axis and the point y=1 What is the area between these two curves? Using the formula A=∫f(x)-g(x)dx

Using the Riemann sum formula: A = ∫ [f(x) - g(x)]dx from a to b Find the area between y=1/2sec²t and y= -4sin²t between the points π∕3 and - π∕3 Please show a detailed solution. Thank you.