Evaluate the indefinite integrals by using the given substitutions to reduce the integrals to standard form. a. √ √x sin²(x³/² − 1), u = x³/² – 1 9x² b. S; dx, u = 1- x³ √1-x³

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Q: At 12:00 noon, there were 200 bacteria present. By 4:00 pm, there were 379 bacteria. If the bacteria…

A: At 12.00 noon, there were 200 bacteria present.By 1:00 pm, there were 379 bacteria.

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Q: Ju udv = Uv -Ivdu to Explain why the substitutions below are inappropriate. Let du: = x dx 1.…

A: We can explain why the substitution is inappropriate in the following steps.

Q: 8 3) If f(x)= 2 (x-1)*, then f (2) (1) = Σ k=0 a) b) 2 c) 4 d1

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Q: E) Evaluate the triple integral on the left in each of the following: (a) ff₁dz dx dy = 1 "dz dy dx…

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Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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A: The given integral is: I=∫sin5xdx   As we know the Power rule: ∫xndx=xn+1n+1+C ; n≠-1

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A: The function f(x)=3 sin(x)+5 cos(x) over the interval 0,π3

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Q: 2- Find the derivative of y with respect to the Exercises 1-3. 6sinh 33 1- -

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A: Given, Amount(A)= $ 51034.26 t= 4 years r= 3.25%= 0.0325 n= 2(semi-anually)

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A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

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Q: Find the general antiderivative of f (x) = O2 ln ln 2x + C 1 O + C - 2 ln 2x O-In In 2x + C 1 O + C…

A: The function is given by fx = 4xlnx2 To evaluate: The most general antiderivative of the function.

Q: Q4/Find x and y that make the equations equal to zero: 5x+2y-4-0 6x+8y-2-0

A: Simplify both equation for x and y .

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Q: 1. Consider the curve y = f(x) = 2* - 1. A. Find the exact area of the region in the first quadrant…

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A: Here we will use the substitution method

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A: The given equation is u" - 4.5u' - 5.5u = - 4sin(3t)

Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

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Q: 1. f(3x + 1)¹5 dx 2. f(8x³ + 2x² - 1)7 (6x² + x) dx x-2 3. f dx √50-5x3

A: LetI=∫(3x+1)15dx put  u=3x+1differentiate du=3dxdu3=dxThereforeI=∫u15du3Take constant…

Q: Evaluate the integral T 22 P" sin cos e de dode Hd 0 H₂

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