(a) Determine whether the integral given is proper or improper(if so, explain why). ~2 1 dx |x – 1| Hence evaluate the integral.

Q: Q.6 Evaluate the integral by interpreting it in terms of area 1) L xdx 2) LV16 - x² dx

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Q: Find the exact value of the integral using formulas from geometry. 10 V100 - x dx 2 10 |100 -x O 00…

A: The objective of the question is evaluate the definite integral.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) ecos(st) sin(5t) dt

A: Given : ∫ecos5tsin5tdt

Q: A definite integral Evaluate In x dx.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) secx tan x dx

A: ∫sec7x tanx dxu = sec7xdudx = 7 sec7x tanxdx = 17 sec7x tanx du⇒17∫1 du= u7substituting u = sec2x=…

Q: Evaluate the definite integrals using properties of the definite integral and the fact that 5 $S² √3…

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Q: Evaluate the indefinite integral. Use C as the constant of integration. de

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Q: Evaluate the definite integrals using properties of the definite integral and the fact that 4. 4…

A: given : ∫-52f(x)dx=-3 , ∫24f(x)dx=8 , ∫24g(x)dx=8(a) ∫-5210f(x)dx=10∫-52f(x)dx=10×(-3)=-30…

Q: Find the general indefinite integral. (Use C for the constant of integration.) x' dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dr

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Q: Evaluate the integral of f(x) = e between x = 0 and x = 1 using Simpson's rule with h = 0.125. Use 6…

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Q: Use an appropriate u-substitution to evaluate the indefinite integral -dt. Use C'for the constant of…

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Q: Explain why f e-a dx cannot be evaluated using u-substitution. Then give an example of a similar…

A: Consider the integral ∫e-x2dx. Suppose u-substitution is possible. let u=x2. This gives,…

Q: Find the indefinite integral. (Use C for the constant of integration.) 1 z6 + dz (8 - z)4

A: integration

Q: a) Use Trapezoidal and Simpson's Rule to evaluate the integral , (2x – 1)dx by taking n=4

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Q: Evaluate the integral using the properties of even and odd functions as an aid.

A: Given: I=∫-22x2x2+1dx let's  fx=x2x2+1 first checking fx is odd or even, for that we put x=-x in fx,…

Q: (c) dx 1 – x2 (d) | Va? + x² dx

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Q: sinx dx e-ax 8

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Q: Evaluate the indefinite integral. (use C for the constant of integration.) dx = 6(8 + gx) %3D

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) XV 1 - x2 dx

A: The integral is given by

Q: Express the integral in terms of the variable u, but do not evaluate it. | 7x /5 – x² dx; u = 5 – a²…

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Q: (e) / V1 + x² dx (f) x² + 4 dx

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

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Q: Evaluate the integral by u-substitution. (Use C for the constant of integration.) Integral of…

A: Given : Integral ∫Sin3(x) cos(x) dx   To find : Evaluate the integral by u-substitution?

Q: Evaluate the indefinite integral. (Use C for the constant of integra 9 dx 8V1- x2

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Q: Evaluate the definite integral. Round your final answer to three decimals. 53 298, 512 dt 38 t3 Vt2…

A: We will evaluate the given integral as shown below

Q: How are integral tables typically used? What do you do if a particular integral you want to evaluate…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sec'x tan x dx

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Q: Evaluate the indefinite integral: 1 dx V 100 – 81x2 %3D

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Q: integral

A: Useful formula: ∫xndx = xn+1/(n+1) + c

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) z2 dz 8 + z3

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Q: (a) /(3=² (За? — 6х + 5) dx - 1 .5 x° + 5 1 (b) dx - 4

A: To determine the value of definite integrals.

Q: Evaluate the integral. (Use C for the constant of integration.) xổ dx

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Q: Determine the value of the integral: integral sign:  (x)(e^-x)

A: Recall the formula for integration by parts:

Q: mpute the integral of f(x) = 3x from a = 0 to b = 9 with 3 sub-intervals using lowing integral…

A: In this question, the concept of numerical integration is applied. Given, fx=3x,a=0,b=9,n=3 The…

Q: Using only the definition of RS-integral, evaluate x* d[x]. 0.

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Q: Integrak of: x(x + 7)^15 dx

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Q: intergrate the integral from 0 to 1 of (x^2 + x + 1)/((x+1)^2)(x+2)) dx

A: See the details solution in below

Q: (2+ln² x) 2. S: -dx x(1-In x)

A: As per rules supposed to solve only one problem at a time so please post the remaining question as a…

Q: Use comparison properties of integrals to make a conclusion about the r16 lower and upper values of…

A: Solve the following

Q: 2-V1-x dx by interpreting the integral in terms of area. -

A: ∫-112-1-x2 dx On simplification, we get ∫-112-1-x2 dx=∫-112 dx-∫-111-x2 dx   →1 Now consider, ∫-112…

Q: Evaluate the indefinite integral using substitution. (Use C for the constant of integration.) dx - 1

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Q: 5 dx. V1– x² 20. Evaluate the indefinite integral /

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | sec2(0) tan²(0) de

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Q: 描 罪 樂 排 Evaluate the indefinite integral. (Use C for the constant of integration.) (3t + 4)2.2 dt

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) /(2 sin(x) dx sin?(x),

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Q: Evaluate the indefinite integral by the method of substitution. Let u = x*. (Use C for the constant…

A: ∫ x31+x8dx =∫x31+x42dx.............(1) take  u=x4 du=4x3dx dx=du4x3...............put it back in…

Q: Svaluate x dx from the definition of RS-integral.

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Q: an appropriate method. 1₁ Evaluate the integral using 1 x²√x² +9 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) x dx

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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.