Graph the integrand and use geometry to evaluate the integral. 19) S (3-1x) dx -3 D A) 27 B) 9 C) 18 Solve the problem. 8. 20) Suppose that f and g are continuous and that f(x) dx = -2 and g(x) dx = 9. 8. | [5f(x) + g(x)] dx . Find A) -1 B) 35 C) 43 D) 14 Compute the definite integral as the limit of Riemann sums. 21) x3 dx -3 81 81 B) D) 0 A) 27 4

Q: Evaluate: a) +7sec2 x dx /x 1+x?

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Q: 8 -8 25 √64-x²-(y-17)² dy dx 11

A: As per the question we are given a double integral which we have to evaluate.We will use the…

Q: 3 Using appropriate substitutions evaluate V9 – x² dx

A: To find : Evaluate the integral given in the question.

Q: = 1- Solve y"+6y' +9y=2xe * + 3 + 2x²

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Prove : (x2 + 2x + 2 )dx > 0

A: The given integral is ∫-10x2+2x+2-x2dx The integral has been rewritten∫-10x2+2x+12x2dx Apply…

Q: Use limits to evaluate the integral. | 7x* dr dx 14 2 O 28 112

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Q: 3) Evaluate using area interpretation, with known geometric formulas (a) [f(x)dx (b) [ƒ(x)dx y=f(x).…

A: ∫04f(x)dx=area of the semicircle=π2r2=π2×22=4π2=2π∫46f(x) dx=Area of the square=-22=4

Q: x? dx 3. J Tx? + 4)²

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Q: Evaluate the integral S√x Inx dx 3 2 4 -x² Inx+ x² + C 03x³nx-x²+c 4 2 -x² Inx+ 2 C 15 3 2 4 °²x²nx…

A: We have to solve above integral

Q: f (x) = [x + 4] df 1 =? dx 8 - O A) 1 В) 10 о с) -1 D) 2 O E) 0

A: The function f(x)=x+4. We have to find dfdx12=?

Q: Evaluate the integral by making the appropriate substitutions. Write your solution as a single…

A: Our Aim is to evaluate the integral given below:-∫03x+2x+1dx -(i)

Q: P4: x3 (x² + 1)3

A: Use the algebraic substitution and solve the integration.

Q: p) Determine | (hVx +r) dx (where h, r are real numbers).

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Q: 1. dx x+2

A: Due to our guidelines I am solving only 1 question

Q: ral L9/x? + y') dxdy.

A: Solution :-

Q: Q2 Approximate this integral using Simpson's rule whose abscissa and weights are given by {-1,0,1}…

A: Please check step 2 for the solution

Q: ニ 2 2. dx | -r

A: The given integral  y=2∫-rrr2-x2dx  Can be solved using integration formulas given below…

Q: d 3) Find 6 '+2t – 9)

A: To find:

Q: d) S 2xe* dx

A:

Q: Jse the symmetry of the function to simplify/evaluate the integral, 3. (2+ |x|5) dx. -3

A: Please refer to the image below.

Q: If fºrex f(x) dx = 12, what is the value of A) 12 B) 0 C) 6 √ [ ƒ(6-x) dx? D) -6

A: If  ∫06fx dx=12, then to determine the value of ∫06f6-x dx.

Q: a) Determine whether the integral da 16 2x is improper or not. Justify your answer. b) Evaluate the…

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Q: e2" – e5r dr dx b)] Jx (1 + x) + e3r

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Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: 1. Evaluate: f (2x+3)dx x²+2x+5

A: As per our guild line we are supposed to answer only one question please repost other questions as…

Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: π Show x² x² + x² +1 4 √3 -∞0 4 Hint: x² + x² +1= (xª + 2x² +1) − x² = (x² +1)² −x² dx =

A: The objective is to show that ∫-∞∞ x2x4+x2+1dx=π3

Q: LEvaluate the integral: 10 – 2x + x²dx. -

A: Since you have posted multiple questions, asper our policy we will answer first question. Please…

Q: dy Find for the given functions. dx3 a) y = /2x + 3 b) y = 2.x – 1

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Q: CoS X F 2x 7x

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Q: If y = ln(x√x² + 1), then A) 1 + X x² +1 B) 1 + dy dx 1 x√x² +1 C) 2x² +1 x√x² +1 D) 2x² +1 x(x² +1)…

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Q: (a) (₁, ₂) (b) (r1,73) (c) (r2,73) r₁= [3 -1 0], (d) r1 xr2 (e) ri Xr3 (f) r₂ × 3 r₂ = [-2 0 1], T3…

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Q: Let W = span{(1,1,-1), (2,3,1), (5,6, -2)}. i Find a basis for W. ii. Determine whether the vector X…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.