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

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Q: Find the following indefinite integral: ∫12x (x2 – 9 )-3 dx. Hint: Use u Substitution.

A: The given integral is ∫12x x2-9-3 dx. Let u=x2-9. This implies that du=2xdx. Substitute these values…

Q: 11. Use definite integrals to show that f(x) = x² – 3 and g(x) = 5 – x² have the same arc length on…

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Q: Find the indefinite integral of the function: f(x) = 1/(x+2)

A: The given function is  f(x)=1x+2

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Q: Find the indefinite integral ∫ (x2 + 8) /x√(x2 − 4)  dx

A: Given that: The indefinite integral ∫x2 + 8xx2 - 4 dx

Q: 3. Discuss the similarities and differences between indefinite integrals and definite integrals.

A: A definite integral is the one that has lower and upper limits and on solving gives a constant…

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

A: Given : ∫xx-55dx

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Q: Evaluate the indefinite integral: ∫x(x2 − 4) dx

A: We know that, ∫af(x)+bg(x) dx=a∫f(x) dx+b∫g(x) dx where a, bare constants , f, gare functions.…

Q: 8. Explain why the formula for the integral of x* does not apply when k = -1. What is the integral…

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A: We have the integral as I=∫x5-x2dx Let us consider that, -x2=t-2xdx=dtxdx=-12dt

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Q: - 1 d.x x11

A: The detailed solution is as follows below:

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

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A: we have to solve integration

Q: Evaluate the definite integrals [(*-2r*) dx

A: Please refer to the image below.

Q: Evaluate the definite integral. (x - 3)(x - 5) dx

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

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

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

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Q: on error among new students of probability, is that they often do this integral, F(x) = /…

A: See the handwritten solution

Q: Suppose we want to approximate the integral | h(x)dx by using a right-hand sum with 4 rectangles of…

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: The integration of the term (76t3-50t-3).

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Q: Find the indefinite integral  (x^5+10)/(x^2)

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Q: Evaluate the indefinite integral. dx x(ln (x))6 (Express numbers in exact form. Use symbolic…

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Q: Evaluate the indefinite integral. x² A -dx 1- x6

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Q: 5 [³ (Use symbolic notation and fractions where neede Calculate the integral, assuming that f(x)dx=

A: topic:- integration

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

A: The given integral is ∫x5-5xx4dx

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A: Consider the integral: I=∫x2+2x-6x4dx……1

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,…

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Q: Find the indefinite integral ∫(x4 + 5x) dx

A: Given: ∫(x4 + 5x) dx Now by using the sum rule, ∫fx±gxdx=∫fxdx+∫gxdx⇒∫x4dx+∫5xdx

Q: Find the general indefinite integral. Illustrate by graph -ing several members of the family on the…

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Q: 1 -8sec Xtonx-9sec?x)dx=>

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Q: Evaluate the definite integral. -4 (10 – 4x) dx 1

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