Use the table of integrals at the back of the text to evaluate the integrals ∫dx/x√(7 - x2)

Q: Use the table of integrals to evaluate the integral. 2 [²³15x³√4x² 15x³ 4x²x4 dx

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Q: Evaluate the integral using the methods covered in the text so far:                    ∫ 7−x dx

A: It is observed that for solving the integral ∫7-xdx,use the substitution method. The substitution…

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

A:

Q: -+inf In(tan¬'x) dx 1+ x2

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Q: Evaluate the integral using the methods covered in the text so far:                    ∫ 2xe4x dx

A: Consider the given integral. I=∫2xe4xdx Put u=2x in the equation. u=2xdu=2xln2dxduln2=2xdx

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫tan-1 x/x2 dx

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Q: Evaluate the integral. integral sign with a 4 at the top and a 1 at the bottom. 8square root of z…

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Q: Evaluate the integral by using a substitution prior to integration /2s + 17

A: Here we have to evaluate,

Q: Use only the fact that is given in function 93, and the definitions and properties of integrals, to…

A: The given function is ∫043x(4-x)dx Now, use property of integrals…

Q: Use the Table of Integrals to evaluate the integral. x² V 4x² - 27

A: ∫341x24x2-27dx=∫341x22x2-332dxLet x=332sec μ .    limits                                  when x=3…

Q: Approximate the integral of: f(x) = Vsin(x) + x* + 5 from x = -10 to x = -14 using N = 4 steps. (a)…

A: Given : f(x)=sin(x)+x4+5 a) using left hand sided rectangles We know that  ∫abf(x)dx=…

Q: 1. x +4 √x -dx

A: We will use substitution method.

Q: Use only the fact that is given in function 93, and the definitions and properties of integrals, to…

A: ∫043x4-x dx=32

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫√(9 - 4x)/x2 dx

A: Using table of integrals  to evaluate the integral ∫9-4xx2dx

Q: 4. dx +

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Q: Use the properties of integrals to choose the inequality that would make the statement true without…

A: We have to choose the inequality.

Q: Evaluate the definite integrals. Requires a supporting analysis. S sva dx

A: Here f(x)=5xwe have to find the value of ∫095x dx∫09f(x) dx=∫095x dx=5∫09x dx=5∫09x12…

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫sin 2x cos 3x dx

A: given: the integral is:∫sin2xcos3x dx let the given integral ∫sin2xcos3x dx be I. as we know that,…

Q: Decide whether the integral is improper. 1,01 In(x5) dx

A: We are asked to find whether integral is proper or improper

Q: (4-x²) dx

A: SOLUTION-

Q: 8. Explain why the formula for the integral of x* does not apply when k = -1. What is the integral…

A: Integration is the opposite process of differentiation. According to power, rule of integration…

Q: It can be shown that f e* dx = e – e. Use this fact and the properties of integrals to evaluate…

A: We have to find

Q: Vhich of the following integrals is equal to the integral f(3x - 5) dr?

A: Use simple integration concept.

Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

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Q: .3 2х — 3 -dx 4 x –x

A: First break the given Integral  Then take 4x- x^2 = u and in other one complete the square  Finally…

Q: Find the formula in the integral table that can be applied to find the integral:

A: Given: The integral ∫25+16x2x2dx, To find: The appropriate formula from the integral table that can…

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫x dx/√x - 2

A: Given Integral is., I=∫xx-2dx

Q: Evaluate the integral. (5x – 4) dx x2 - 13x + 42 (Use symbolic notation and fractions where needed.…

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Q: Evaluate the integral using the methods covered in the text so far:                    ∫ (7 − e10x)…

A: Here we have to evaluate I=∫(7-e10x)dx

Q: Use the Table of Integrals in the back cover of Stewart's text to evaluate the integral -1x4 dx Vx10…

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Q: Evaluate the integral and interpret it as a difference ofareas. Illustrate with a sketch. ∫-12  x3…

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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 using the formulas in the summary and Eq. (1).

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

A: Let,

Q: sin 20 23. do Vcos*0 + 4

A: Explanation of the solution is given below...

Q: x2 dx J x2+4x+5

A: Given integral, ∫x2dxx2+4x+5 To find the value of this integral.

Q: Evaluate the indefinite integral by using the substitution u = 5-x' to reduce the integral to…

A: Given the integral

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫x cos-1 x dx

A: Given: I=∫xcos−1xdx

Q: Evaluate the integrals using the substitution method of 3x2(x3-4)9 dx

A: Given: Let I=∫3x2x3-49 dx To Find: To evaluate the given integration using the substitution method.

Q: Use the Table of Integrals to evaluate the integral.  ∫01x4e-x dx

A: Given:∫01 x4 e-x dx∫u dv=uv-u'v1+u"v2-u'''v3+u''''v4-.......

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. 1 | 3…

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Q: Use the table of integrals at the back of the text to evaluate the integrals ∫x dx/(2x + 3)3/2

A: ∫x2x+332dx Put, 2x+3=t⇒21+0=dtdx⇒2 dx=dt⇒dx=dt2

Q: Evaluate the following integral by using appropriate method. an 3x2 dx x² -25

A: Given:  f(x) =∫3x2x2-25dx                   =3∫x2x2-25dx      By using trignometric substitution Let…

Q: |(3x3 – 2x² + 1) sinh 2x

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Q: Evaluate the integral of the following using Miscellaneous Substitution X Sdx 1+x 5.

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Q: 1. (x² – 4x +4)x

A: Given:       ∫x2-4x+443dx    =∫x-2243dx     =∫x-283dx  substitute u=x-2→dudx=1→dx=du        =∫u83du

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

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Q: -32 1 ย X

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Q: Use only the fact that is given in function 93, and the definitions and properties of integrals, to…

A: Use only the fact that is given in function 93, and the definitions and properties of integrals, to…

Q: Evaluate the integral, if it exists. If it does not exist then explain why. ' 10 x² – 4 -dx 2

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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.