Below are attempts at u-substitution by students. Explain where each student went wrong, then explain how to solve the problem. (b) John is attempting to solve Thus, - √x – 1 dx = - S [²√u du = f ² 1 √x- x-1 dx, and identifies u = x-1, so du = dx. du = [²³1³/²] 2 = ² (2³/²) – ² (1³/²) = }(√8 – 1).

Q: 7. Find d²y dx² from y = √√x- =√x-²/2

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Q: Differentiate. y= In [(x +2)° (x + 5 (x+ 7)°] [In [x+ 2)° (x +5)*(x + 7) ]] =O dx

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Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: 2 3 Find 3/7 ) da 6x2 | _ -

A: We need to evaluate the following integral ∫6x2-2x+3x5-3xdx

Q: 3) Solve the following using the substitution rule. Show all steps in Find [30x(3x²-1)dx

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Q: 5. Solve for x² − x+6 x³ + 3x 1³ dx.

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Q: How do you know your answer is correct? 6 BOTTOM LINE QUESTION Using Formula 2, find the arclength…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 4) Evaluate 2 √x√x² +1 dx

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Q: √√3 tan-¹x 4. (10 points) Evaluate SY 1+x2 dx (using substitution).

A: The value of the integral is 7 pi^2 / 288.

Q: ۱۴ 14 g 3 3+1x 1= x² + 1× AND -FIND /dx WHEN X=2 =6.

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Q: Se е 4x cos(3x)dx

A: The given integral is in the form of ∫udv, where u = 4x and dv = cos(3x) dx. This form is suitable…

Q: Find: Sx³. (x* + 2)3 dx

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Q: then dy dx y = tan -1 ¹ ( √7x² − 1),

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Q: 1 dx x2 + 9

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Q: (a) / | Va? (а) /a² + x² dx

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Q: 1 14) Find xe™³x² dx . | 0

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Q: (4 - x*)3/2 dx

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Q: x² 1- x6 dx

A: Explanation of the answer is as follows

Q: 5 dx J (x - 1)(x2 + 4)

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