Suppose we want to approximate the integral | m(x)dz by using a left-hand sum with 4 rectangles of equal widths. Write out this sum, using function notation for each term. Answer: Now, approximate the integral | m(x)dz by using a right-hand sum with 3 rectangles of equal widths. Write out this sum, using function notation for each term. Answer:

Q: Find the integral of: Зx2 — 4 - x2

A: From the given problem:   I=∫3x2-4x2dx ....(1) Now simplifying: 3x2-4x2=3-4x2 Now substitute this…

Q: Evaluate the following and use change of bounds for definite integrals when appropriate.

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Q: Use substitution techniques and a table of integrals to find the indefinite integral. xp- Vx -1

A: follow next syep

Q: Use substitution to find the indefinite integral. 6 10(1

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Q: Evaluate the definite integrals using the graph of f (x) below. 4- y 2- 2 10 12 -2- -4- -6. (a) I f…

A: Given : The graph To determine :    (a) The integral  ∫02 f(x)  dx .  (b) The integral  ∫24 f(x)…

Q: Solve the integrals using appropriate substitution.

A: Solving the problem by method of substitution.

Q: Evaluate the integral such that the graph of ƒ is shown. f(x) dx 3 2 - -2 4 -1- -2 Round the answer…

A: Since you have asked multiple question, As per our policy we will solve the first question for you.…

Q: 3dx 2. S (x+2)√x²+4x+3

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Q: Evaluate the integrals

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Q: Find the indefinite integral x3(sqrt(1+16x2)

A: Given

Q: evaulte the indefinite integral 1/(5x+6sqrt(x))

A: To integrate the given expression by an appropriate substitution

Q: Evaluate the integral below using summation formulas and sum rules. (x² – 2x)dx 2

A:

Q: Suppose ƒ is an even function with integralEvaluate each integral.

A: Given:           f  is  an even function.    ⇒  f(-x) = f(x)   for all x

Q: Find a formula for the indefinite integral of xneax for n≥1

A: Express the mathematical expression for integration by parts. ∫udv=uv-∫vdu The order of integration…

Q: x+3 x+1

A:

Q: Evaluate the definite integral. -2 (и — 1)? dz

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Q: Determine, with justification, whether the integral below converges or diverges. dx x15-|sin a|…

A:

Q: dx 15. x1+(In x)*]

A: Given:       ∫10dxx1+lnx2       =∫101x1+lnx2dx substitute u=ln x→dudx=1x→dx=xdu…

Q: Find the indefinite integral. (- x/x - 55 dx

A: Given : ∫xx-55dx

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

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Q: 2. (4x³-3)dx

A: Let's find.

Q: хах x2+x+1

A:

Q: (x² – 2x)dx 3. 2.

A: Sum rule states that if you have two functions, then the sum of their integrals always equals to the…

Q: Find the indefinite integrals of the following functions. 7x²

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Q: Find the integral: x45-x5 dx

A: The objective is to find the integration.

Q: Suppose a definite integral has lower and upper bounds as follows. 7.006 < < 7.018 If the midpoint…

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Q: Find an integral expression equal to: lim +2 k=1

A: limn→∞ ∑k=1n2nk3+22n Here, fx=x3+2 &amp;∆x=2n=2-0n⇒a=0 &amp; b=2   ∵∆x=b-an

Q: Use substitution to find the indefinite integral. (9+7 In x)

A:

Q: Evaluate the indefinite integral:  x3ln(x2-1)dx

A: Given integral By using the following substitution, we get

Q: Find the indefinite integral by using the substitution x = 2 tan(0). (Use C for the constant of…

A: Given ∫2x24+x22dx and x=2tanθ

Q: Evaluate the definite integrals using the graph of ƒ (x) below. 4- y 2- 2 4 10 12 -2- -4- -6- •4 (a)…

A: Given,

Q: eln x -dp- x(elnx + 3)

A:

Q: Use a table of integrals or other techniques to solve the following indefinite integral. xp: x -64

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Q: Evaluate the indefinite integral. x4/(1+x10)dx

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Q: How to solve the integral of (x+2)/(x+4)? Apparently division with rational functions is required

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Q: Write the integral as the sum of the integral of an odd function and the integral of an even…

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Q: Evaluate the integral below using summation formulas and sum rules. 3 (x2 – 2x)dx

A: Given integral is  ∫23(x2-2x)dx We know that, ∫(f(x)-g(x)) dx=∫f(x) dx -∫g(x) dx              Using…

Q: Evaluate the definite integral

A: Evaluate definite integral.

Q: Suppose a definite integral has lower and upper bounds as follows. 8.009 f(x)dx < 8.012 If the…

A: We will find approximate value of integral and then find maximum difference between approximate…

Q: Determine whether the integral is convergent or divergent. 8. 78 dx (x - 6)3 O convergent divergent…

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Q: Find the indefinite integral. x° - 5x xp. 4 X° - 5x dx = 4

A: The given integral is ∫x5-5xx4dx

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation…

A:

Q: 1+x

A:

Q: Find an integral expression equal to: lim +1 k=1

A: The given expression is, I=limn→∞∑k=1n2nk+33+12n In general, the Reimann sum can be written as,…

Q: Find the indefinite integral.   xe^6x/(6x+1)^2dx step by step

A: We will use integration by parts

Q: Evaluate the integral.

A: Integral:∫2xxdxLet, x=z      12x dx=dz

Q: x'-6x+9 3. S

A:

Q: x-1 マーメ-1 ーズ

A: