area of the region. y1 = x2 + 2x + 2 y2 = 2x + 11

Q: Q3 Shade the area of the region bounded by, x² + y² p Hence, find the area of the specified region…

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Q: Determine the value of the integral Integral sign: ((z^2 + r^2)^-3/2)x((2r)dr)

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Q: Evaluate the integral. (Use C for the constant of integration. x² 3/2 dx - 4x²)2 3 + 4x

A: We have∫x23+4x−4x232dx

Q: 3 Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

A: Giv

Q: Find the area bounded by the parabolas x2+y-9=0 and x2-8y=0   (SOLVE BY USING INTEGRAL CALCULUS)

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Q: y = 2 – x2 ; y =-x

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Q: Find the area of the region. 5ex y = 1 + e2x y 4 3 x = In V3 2 1 -2 -1 2)

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Q: Solve for the area between y = x² – 8 and y = x from x = -2 and x = 2.

A: The formula to find the area between the curve f(x) and curve g(x) on an interval [a,b] is given…

Q: Shade the area of the region bounded by, x² + y2 < 7² and |x| + |y| 2 7 Hence, find the area of the…

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Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: 3. Find the area of the region bounded by y = x², y = 8 - x² and y = 4x + 12.

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Q: 1= y - 4y (-3, 3) z = 2y – y -1.

A: Given the query is to find the area bounded by the curve.

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 16 +…

A: Integration by parts:∫uvdx = 4∫vdx - ∫[ddx(u)∫ vdx]dx

Q: Use a double integral to find the area of the region. The region inside the circle (x − 3)2 + y2 =…

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Q: |x| dx 1 X V1– x² -1

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Q: The area between y = 3 x + 1 and y = x² from x 1 to x = 3 is II %3D

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Q: 1 dx 1 – x?

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Q: Find the area between y=x+2 and y=3x2+x for 1≤x≤2.

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Q: Find the area of the region between y² = x and x = y +2.

A: Given,  y2 = x   and  x = y+2  We have to find the area of region between y2 = x   and  x = y+2

Q: X' 2 -1 Vx * dx X,

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Q: Evaluate the integral dx (x + 1)(x² + 1) Sz

A: The integrand can be written as:…

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: Evaluate the integral. (Use C for the constant of integration.) | (4x4 - 3x-2 + 5x-5 + 2) dx

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Q: Shade the area of the region bounded by, x2 +y2sp2 and |x| + |y| 2p Hence, find the area of the…

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Q: Use a double integral to find the area of the shaded region. -2 π/2 6 2 2 -4 -6 r=3+3 cose 2 4 0

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Q: Sketch the region whose area is given by the definite integral. 36 - x2 dx y y 12 35 30 25 20 15 10…

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Q: Find the area between the Y=2x-x² and y=-x.

A: Given curves y=2x-x2 and y=-x We have to find the area between the curves.

Q: Determine the area bounded by: y2-12y-8x+28=0; and x2-4x+4y-20=0

A: The given equations: This can be rewritten as, To find the area bounded by the above equations:…

Q: Is the integral of 2x wrt x equal to 2x^(1+1)/(1+1)?

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Q: Find the area of the region bounded by x = y² and 3y = 2 +x

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Q: T/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5 - 10

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Q: Evaluate the integral. (Use C for the constant of integration.) (4x4 3x-2 + 5x-5 + 2) dx

A: By using integration formula we can easily solve it. See attached file for a step by step…

Q: Evaluate the integrals: 1. 2. -2 dx 0 8+2x² x+3 2x3-8x S - dx

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Q: Find the area of the region between y=x^1/2 and y=x^1/3 for 0≤x≤1.

A: the area of the region between y=x^1/2 and y=x^1/3 for 0≤x≤1.

Q: Set up the definite integral required to find the area of the region between the graph of y = 17 – r…

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Q: Evaluate the integral ∫dz/1 + ez

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Solve for the area of the region bounded by: x^2 = 4y + 4 and x = y - 2

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Q: Use a double integral to find the area of the shaded region. n/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5…

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Q: Evaluate the integral. V3 9earctan(y) dy 1 + y2

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Q: Find the area of the region between x = y3 and x = 3y — 2.

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Q: Find by double integration the area bounded by the given curve, y2 = 4x & y = 2x - 4

A: If a region is bounded by the curves f(y) and g(y) over the interval [a,b], then the area by using…

Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and…

Q: Find the area of the region that is enclosed between y=4x^2-x^3+x and y=x^2+3x.

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Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

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Q: Find the area of the region between y2=x and x=y+2

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given by…

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

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Q: Evaluate the integral using tabular integration by parts. 1 | 7 x° V2 x+1 dx (2x + 1) (35x – 15x? +…

A: Given,            ∫7x32x+1dx

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 5 Y2 = 2x + 30 %3D…

A:

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.