1) a) Find and -1 b) Using a graph, explain why the first integral in (a) gives the area, whereas the second integral does not.

Q: Evaluate the integral by interpreting it in terms of areas. -х 3) dx

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Q: Graph the integrand and use known area formulas to evaluate the integral. 1 |x| dx -5

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Q: d. Integrate your integrals from parts c and d and show that the two integrals give the same area.

A: Given equations are: y=x2 and y=4 The integral representing area bounded by two equations with…

Q: Which integral would represent the area shown?

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Q: 29) Find the area bounded by the curves y= In x, y = 2 In x and line x-e in the first quadrant.

A: I have given the answer in the next step. Hope you understand that

Q: evaluate the integral by interpreting it in terms of areas

A: The given integral is,

Q: cosa drdy =?

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Q: Graph the integrand and use known area formulas to evaluate the integral. 2 |2x| dx .....

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Q: What integral(s) can be used to find the area bounded by  the graphs of  y = − x + 3 and y = 4/(x +…

A: y = − x + 3 and y = 4/(x + 2) We need to determine the integral which can be used to find the area…

Q: Evaluate the integral by interpreting it in terms of areas.

A: Let the given integral be y - y = ∫-442x-16-x2dxy = 2∫-44xdx - ∫-4416-x2 dxy = 2∫-44xdx - ∫-4442-x2…

Q: Evaluate the integral by interpreting it in terms of areas. 3 dx

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Q: - Evaluate the integral by interpreting as an area:

A: We have to find the integral ∫-111-x2dx.

Q: Apply trapezoidal and Simpson's rules to the integral

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Q: Using iterated integrals, find the area bounded by x2 − 6x + y = 0 and x2 − 2x − y = 0.

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Q: Evaluate the integral by interpreting it in terms of areas. 5 + 81 x2 ) dx

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Q: y =x, 4x + y =12

A: Let's find.

Q: Evaluate the integral using integration by parts. 40 sec 20 do

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Q: graph the integrands and use known area formulas to evaluate the integrals.

A: We need to graph the integrands and Use the formulas to evaluate the integral.

Q: Evaluate the integral by interpreting it in terms of areas. 49 -x²) dx Need Help? Watch Read it

A: Given :∫-702+49-x2dx

Q: Determine the integral by interpreting it in terms of areas. 2x

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral [ sqrt 4 + (In…

A: Given: ∫x+lnx2xdx

Q: Evaluate the integral by interpreting it in terms of areas. 9. |x| dx -5

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Q: Find the area bounded by y^3 = x^3 + x^4 and the x-axis. Sketch this and label the important…

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Q: Which of the following integrals, if any, calculates the area of the shaded region?

A: Given graph,

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 5  dx

A: Split tan5x into simpler powers tan3x and tan2x and change tan2x to sec2x-1 and simplify.…

Q: Evaluate the integral by interpreting it in terms of areas: xp |xJ

A: The given integral is ∫-22xdx. The limit of x lies between -2 and 2. The integrand is the function…

Q: 1. Sketch and find the area bounded by the graphs of y =-x x and y =

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Q: 7 - over the interval [1, 5] Find the area under the curve y

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Q: Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to…

A: Given query is to find the value of the integral

Q: Set up the integral to find the area inside the graph of r = 2 + sin 0. %3D

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Q: Graph the integrand and use areas to evaluate the integral. V 25 – x² dx - 5

A: Given,          ∫-5525-x2dx

Q: Evaluate the integral below by interpreting it in terms of areas in the figure

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Q: Evaluate the integral by interpreting it in terms of areas: [*(5-32) dx =

A: Lets sketch the graph of  f(x) = 5-3x and add the vertical lines x=0 and x=4  we get

Q: 4) Write a definite integral that represents the area of the shaded region and compute the integral…

A: Given the equation of the line is y=-x+4 Intersection with x-axis: Put y=0 0=-x+4x=4

Q: Set up (but do not evaluate) definite integrals for the area of the triangle with vertices (0, 0),…

A: Topic :- Application of integration

Q: 6. Compute the area enclosed by the curves y = x² - 9 and y = 9-x2. Page 5

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Q: Find the area under the curve y 6x* over the interval (0, 4 Submit Question

A: Given that  y=6x^4 on[0,4] To find the area under the curve

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral [ sqrt (e2x   -…

A: Given:     ∫e2x−1dx

Q: 5 -over the interval [4, 7]. Find the area under the curve y = (3x + 1)? Enter the exact answer.…

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Q: а. Calculate the area under the curve from -2<x<2 using four inscribed rectangles. b. Calculate the…

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Q: Evaluate the integral by interpreting it in terms of areas. (10 – 5x) dx

A: Explained below

Q: Evaluate the integral by interpreting it in terms of areas. (6 – 2x) dx -3

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Q: 23. Show that the circumference of the unit circle is equal to dx (an improper integral) Evaluate,…

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Q: Evaluate the integral by interpreting it in terms of areas: (6 – 4x) dx =

A: Given: ∫-226-4xdx To find: We have to find the integral by integrating it in terms of areas.

Q: Solve using iterated integrals. (with graph) Find the smaller area cut from the circle x2 +y2 = 25…

A: The objective is to find the smaller area cut from the circle x2 +y2 = 25 and x=3.

Q: Evaluate by  ∫01  x   √ (1- x4)   dx  by making a substitution andinterpreting the resulting…

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Q: Evaluate the integral using area formula:

A:

Q: Evaluate the integral by interpreting it in terms of areas:

A: When,

Q: Which of the following integrals would compute the area inside the inner loop for:

A: First we have to calculate bound for the given function. Then we can determine the integrals

Q: Evaluate the integral using the FTC I.

A: Solution