52. Use Property 8 to estimate the value of the integral 1 dx Jo 1 + x2

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: Evaluate the integral.  integral  cot  3 x   dx

A: Consider the given indefinite integral: Here the objective is to find the indefinite integral of…

Q: Give a geometric argument that explains why the integrals have equal values.

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Q: Evaluate the integral. 6. 6 cosh (x) dx X, 4

A: Let x=u Differentiating both sides with respect to 'x', we get ddxx=ddxu12x=dudxdxx=2du

Q: Evaluate the integrals ∫tanh 2x dx

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Q: Find the exact value of the integral using formulas from geometry. 5 (3+ 2x)dx 1

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Q: Evaluate iterated integral.

A: We have  I=∫34∫126x5+yx dx dy   Integrate with respect to x. We get I=∫346x25×2+ylnx12…

Q: ez tanh dx

A:

Q: 1 use this fact and the properties of integrals to evaluate dx =3 (7 – 6x2) dx. Given that

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Q: Tt/3, S (sin x – sec²x) dx

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Q: Evaluate  integral.

A: The given integral ∫273+5yxdy can be evaluated as, ∫273+5yxdy=1x∫273+5ydy…

Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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Q: Evaluate the integral. 6 dx 16

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Q: Use any method to evaluate the integral. 8 dx (16x? + 1)?

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Q: xe dx

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Q: Find the following indefinite integral. |(5sin(y) + 4sec(y)tan(y))dy

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Q: Evaluate the indefinite integral given below. [6e¹tan (2) Gett 6e4 tan (2x) sec² (2x) dx

A: The given integral: ∫6e4 tan2xsec22xdx

Q: Evaluate the integral.  integral y 3 sqrt (y 2 +1 )dx

A: We have to evaluate the integral: ∫y3y2+1dy We will use substitution method to solve this integral…

Q: Evaluate the indefinite integral: (8e" + 5 sec? u) du =| + C.

A: We use integration of eu=eu and integration of sec2u= tanu .

Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

Q: Evaluate the integrals below: 1 2y .dx cos3x а) .dx, b) 0. lelsin3x – 1)

A: Here I am attaching image so that you understand each and every step.

Q: 5 .Use the definition of the integral to evaluate | (2x - 3)dx

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Q: Evaluate the double integral : (y – 10x) dr dy

A: To evaluate the given double integral.

Q: Find a new variable u in integral

A: The integral ∫4x3x4+510dx=∫u10du. We have to find the new variable u.

Q: sketch, reverse and evaluate the integral dy dz 15

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Q: 2. +4) dx

A: Given: ∫02x2+4dx

Q: calculate the integral.

A: Let,

Q: Evaluate the integral. La – 4x)dx

A: We have to evaluate the value of It can be written as

Q: 1 dx = 2 Jo 4+x 8.

A:

Q: Show using residues that   the integral from 0 to infinity of dx/(1+x^6) equals (2pi)/3

A: We have to show that ∫0∞dx1+x6=2π3 by using residue theorem. Now, ∫Cdz1+z6=∫−RRdx1+x6+∫γdz1+z6 Now,…

Q: In 13 cIny ex+y dx dy. Evaluate the integral The value is| (Type an exact answer.)

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Q: 1 dx = 2 o 4+x'

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Q: Use Property 8 to estimate the value of the integral.

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Q: Use substitution to find the indefinite integral. 4x° e 4x* dx .3 e 4x* dx =

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Q: Evaluate the indefinite integral: dx + C. %3D 6x4

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Q: cln 2 tanh 2x dx

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Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: the sketch, Evaluate & reverse of integral 3. dj dx

A: Definition used- Reverse the order double integral – In double integral, we can reverse the order of…

Q: Evaluate the improper integral : [° 6x°e¬9æ° dx

A: To solve this question assume 6x^5 = t

Q: Evaluate the indefinite integral: (3e" + 6 sec? u) du: |+ C.

A: As per guide line we have

Q: Calculate the following integral Jo dx 4-x2

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Q: Use the substitution x = 6 tan(0) to evaluate the indefinite integral 91 dx X²VX2 + 36 swer = +C

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Evaluate the improper integral. x In6x dx 0.

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Q: + 3x dz. x2 + 1

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Q: determine Ahe impraper integral dx (H+1)(x²+1)

A: ................(1) use the partial fraction  ................(2) ................(3) take x=-1…

Q: Sec?(sx +8) dx=

A:

Q: Evaluate the integrals ∫tan (ln y)/y dy

A: Given ∫tan(ln(y))ydy

Q: Evaluate the integral. x sec (8x) dx + C

A: