Evaluate by  ∫01  x   √ (1- x4)   dx  by making a substitution andinterpreting the resulting integral in terms of an area.

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

A: We know that the area of right angle triangle is :  A = (1/2) × base × perpendicular

Q: Evaluate the integral by interpreting it in terms of areas. 3 + V 25 – x² ) dx -5

A: First Method

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 integral using the following values. 6. dx = 4 x3 dx = 320, x dx = 16, 6. x³ – 2x + 9 )…

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Q: (x²-x)dx

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Q: (x³-4x) dx

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

A: Given,   ∫-12x3dx

Q: Evaluate the integral using the following values. [x dx = 16, x3 dx = 320, dx = 4 | (8x3 - 12x + 9)…

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Q: Use the Table of Integrals to evaluate the integral.

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Q: Evaluate the integral by interpreting it in terms of areas. La- (1 — х) dx

A: Solve the integral using figure.

Q: Evaluate the integral by interpreting it in terms of area. 4 V16 – x dx

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Q: Evaluate the integral by interpreting it in terms of areas. /1 – x² dx

A: The given integral is as follows- I=∫-101-x2dx The given integral is a graph of quarter circle with…

Q: (2+ v25 – r²) dr = /25 – 3 dx = -5

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Q: evaluate the integral using the methods covered in the text so far.

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

A: Area

Q: Evaluate the Integral using the following values. [x³ dx = 260, [°x dx = 10, [° dx = 2 L 122-…

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Q: Evaluate the integral by interpreting it in terms of areas. La '5 (1 – x) dx

A: The solution is:

Q: (4-x²) dx

A: SOLUTION-

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

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Q: Evaluate the following integral by interpreting it in terms of areas: (1+ V9 - x²) dx 6.

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Q: Evaluate the integral by interpreting it in terms of areas.  integral 0  to 9  (1/3 -2)dx

A: given that integral 0  to 9  (1/3 -2)dx We need to evaluate the integral by interpreting it in terms…

Q: Evaluate the definite integral by interpreting it in terms of areas. | (2x – 16)dx

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

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Q: Evaluate the following integral by interpreting it in terms of areas: |æ| dx -1 Value of integral =

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Q: Using only the definition of RS-integral, evaluate 2 d[x}.

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Q: Evaluate / av1 – aª dæ by making a substitution and interpreting the resulting integral in terms of…

A: Firstly we will find the definite integral after that fill the limit  I =  ∫ x*sqrt(1-x4) dx…

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: Evaluate the integral | r – 3| dx by interpreting it in terms of area.

A: Formula for integrating modulus function:

Q: Evaluate by  ∫-2 2  (x +3 )  √ (4- x2)   dx    writing it as a sum oftwo integrals and interpreting…

A: Given: I=∫-22x+34-x2dx we know that ∫abfxdx=∫abfa+b-xdx…

Q: Evaluate the Integral using the following values. -206 [³x² dx = 260, [°x dx = 10, [° dx = 2 (22-7x…

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Q: evaluate the integral using the methods covered in the text so far.

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Q: Evaluate the integral by interpreting it in terms of areas. 2) dx

A: Given the definite integral I=∫09(13x−2)dx

Q: dx 6. xVa² - x² X

A: Consider x=asinu. Differentiate the equation x=asinu and simplify to calculate the value of dx.…

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

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Q: Evaluate the integral by interpreting it in terms of areas. (1 — х) dx

A: Please refer the attached image for complete solution. THANK YOU.

Q: Evaluate the integral by interpreting it in terms of areas. La - « (1 — х) dx

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Q: Evaluate the integral using the following values. [₁x³ dx x³ dx = 960, ["x dx = 24, "dx = 4 [² (2x -…

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Q: 1. Evaluate (2 – x) dx by drawing a picture and interpreting the integral in terms of areas.

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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: Evaluate the integral using the following values. 9. x3 dx = 320, 9. dx = 4 dx = 16, %3D - 10x + 3)…

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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: 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 -7 to 6   (1-x) dx

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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: Compute the indicated integral by findng the area of the trapezoidal figure below. 110 4,0 F1 10 •5…

A: Given: A=∫35x+3dx

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

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Q: Evaluate the integral using the following values. 8. x dx = 1,020, x dx = 30, dx = 6 1. 8x 10

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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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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.