Consider the area between the graphs x + 2y = 29 and x + 6 = y?. This area can be computed in two different ways using integrals. The area can be computed as a sum of two integrals,

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: Evaluate the integral by interpreting it in terms of area. integral -3 to 0(1+(9-x^2)^1/2)dx

A: Let us assume y=1+(9-x2)12 y-1=(9-x2)12(y-1)2=9-x2x2+(y-1)2=9This is an equation of a circle with…

Q: Evaluate the integrals ∫tanh 2x dx

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Q: By using double integrals find the area between x = – y², lines y = x – 4, y = -2 and y = 2.

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Q: Evaluate the integral using tabular integration by parts. (3 x² – x + 1) e¬¤ dæ +C -

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: 2 B. Evaluate | (2- x) dx by interpreting the integral in terms of area. -1

A: Topic = Integration

Q: Evaluate the integral and interpret it as a difference of areas. 2 x³ dx

A: Given,   ∫-12x3dx

Q: 37. x² In x dx

A: To evaluate the integral ∫1e2 x2 ln x dx using integration by parts.

Q: Evaluate the integral by interpreting it in terms of areas: (2) [+ |x|dx (1) L₂ (3+√4-2²) dx

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Q: 2. Sketch the region whose area is given 25 by the definite integral Jo V25 – x² dx and then use a…

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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 integrals ∫tanh x/7 dx

A: Evaluate ∫tanhx7dx

Q: Evaluate the integral by interpreting it in terms of areas. 3 (4 − 2x) dx   −5

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Q: Approximate the integral from 2 to 14 (x2 -5)dx using 4 rectangles

A: To find the area under the curve using rectangles, the Reimann sum is used.First, we need to find…

Q: 8. Evaluate the integral x-1 dx by interpreting it as an area.

A: Area

Q: Use the properties of integrals to evaluate integral 0 to 1 (4+3x2 ) dx

A: Given: I=∫014+3x2dx for evaluating given integral, first we separate terms then integrate it

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

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Q: Use the value of the first integral I to evaluate the two given integrals. 3 | - 27 (x3 - 6x) dx =…

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Q: 2. +4) dx

A: Given: ∫02x2+4dx

Q: Evaluate the integral by interpreting it in terms of areas. 4 + V 81 x2) dx

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Q: Use a double integral to find the area bounded by y = x², y = -x+ 12, and y = 4x + 12.

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Q: find the indefinate integral of (x^8+18)/x^7 dx

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

A: Given graph,

Q: Evaluate the integrals using integration by parts. ∫(r2 + r + 1)er dr

A: We have to integrate using integration by parts: ∫r2+r+1erdr When two function is in product then we…

Q: Find the area represented by the definite integral. 13 |x- 10| dx

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Q: 4. Evaluate S,(x + 3)v4 – x² dx by writing it as a sum of two integrals and interpreting one of…

A: Given integral is ∫−22x+34−x2dx First , we will write the given integral into sum of the two…

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

A: We know a simple integration gives us the value in terms of the area only. Hence, we only need to…

Q: Use a double integral to find the area of the specified region. 25 y = 25 - x 20 15 10

A: Use double integral

Q: Set up the definite integral required to find the area of the region between the graph of y = 15x +…

A: here i am giving my handwritten solution.

Q: Evaluate the integral by interpreting it in terms of areas •5 (x – V 25 – x?) dx -5

A: Given,  ∫-55x-25-x2dx

Q: Evaluate the integral by interpreting it in terms of areas. 2 + V 81 – x² ) dx 6-

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Q: Evaluate the integrals using integration by parts. ∫p4e-p dp

A: ∫p4e-p dp

Q: Find the area bounded by y = (11-x)1/2 , the lines 3x = 2 and x = 10, and the X-axis.   (Solve…

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Q: .2 32. 8x dx, x > 8 -

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Q: 28. X (1+4x²)³ dx

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Q: Evaluate the integral by interpreting it in terms of areas. V 25 - x2 ) dx

A: Given that, The integration is the following, I = ∫-50(4+25-x2)dx We have to find the value of this…

Q: The area bounded by the small loop of the limaçon r = 1 – 2sin0 is given by the definite integral

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

A: The integral means the area under y=1-x from -1 to 2

Q: Evaluate the integral by interpreting it in terms of areas. *18 |x - 9| dx

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Q: (2г — 1) dr

A: Given ∫-132x-1dx

Q: Find the area represented by the definite integral. 12 |x-11| dx

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Q: Evaluate the integral using tabular integration by parts. 2 x³ /2 x+1 dx +C

A: Recall the tabular integration by parts

Q: Evaluate the integral by interpreting it in terms of areas.  integral-1 to 2 (1-x)dx

A: ∫-121-x dx It can be written as, ∫-121-x dx=∫-111-x dx+∫121-x dx Now ∫-111-x dx represents an area…

Q: Evaluate the integral by interpreting it in terms of areas.  integral 0 to 10    (|x-5|) dx

A: Given  The integration is I=∫010x-5dx

Q: Evaluate the integral by interpreting it in terms of areas.  integral -7 to 6   (1-x) dx

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Q: Evaluate the integral using tabular integration by parts. |(4 2 – x + 2) e* de +C

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 4 +…

A: Given

Q: Evaluate (x + 3) V16 - x2 dx by writing it as a sum of two integrals and interpreting one of those…

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx 4 + (In(x))?

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Q: Evaluate , (x + 3)/4 – x² dx by writing it as a sum of two integrals and interpreting one of those…

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