evaluate the integral. a-) x2 2x dx c.) b.) 3 )عو ه dx 5/3

Q: Evaluate the integral, if it exists.  ∫Csc2 (3t) dt

A: ∫ cosec23tdtLet 3t=θ⇒ddt3t=dθdt3=dθdt⇒dt=dθ3-1

Q: Noting the range of the integral, compute .2 Jo (2² + 9)2dx.

A: By using inequality of integration

Q: +9 =zxe %3D

A:

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integral: , (V4-z² dydz O 2[1- 4] + c O 2 [1 – ±] et

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Q: Express the integral in terms of the variable u, but do not evaluate it. In c dr; u = In x rels In c…

A: To determine: where  u = lnx

Q: Express the integral in terms of the variable u, but do not evaluate In a u= In a In r du %3D

A:

Q: Evaluate the integral: (In z) dz =

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Q: Evaluate the integral by making the given substitution. sec(6z)tan(6æ)dr, u = 6z + C

A: According to question given :∫sec6xtan6x dx, u=6xWe have to evaluate the integral by making the…

Q: Evaluate the impropec integral oc sho that it diverges, dx

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2…

A: Given:

Q: Evaluate the integral.

A: Given: ∫e6dxxlnx. for finding this integral we use substitution method and  substitute lnx=t now we…

Q: Find the anc length oF t1x)=x° on [o,] Hint; use the Integral Tables,

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Q: Evaluate the integral S(in 7x)? dx

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Q: Evaluate the integral using FTC I.

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

A: ...............(1) substitute put it back in equation 1

Q: Compute the integral 2u? du u² – 1

A: As per our guidelines we are supposed to answer only first question. Kindly repost other question as…

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (5x² +…

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Q: Use Trapezoidal and Simpsons 1/3 rule to estimate integral ( - 2x° + 7x - 5) de.

A: The expression ∫13x3-2x2+7x-5dx. We have to use Trapezoidal and Simpsons 13 rule to estimate the…

Q: Evaluate the integral.

A: Let the given intergral be y -y = ∫01r34+r2dry = ∫01r24+r2 r drLet,x = r2Diffrentiating with respect…

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x2 +…

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Q: dx (x + 2)3

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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: the exaet V alde Of the integral. a

A: The objective is to show the exact value for the integral, ∫01axdx This can be re written as,…

Q: O Evalu ake I dx

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Q: Evaluate the integrals in Exercises 45. tanh dx 46. coth de

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the integral t5sin

A: let  I=∫t5sin(t6)dtsubstitutet6=udifferentiate6t5dt=duort5dt=16du

Q: Use the indicated substitution to evaluate the integral. Jese 63csc (7x)cot (7x)dx, u=7x 63csc…

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

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Q: COSz Show, without evaluating the integral, that z2(z + 1) *26 5 zp-

A: Given integral is , ∫ccoszz2z+1dz. Cauchy residue test: ∮fzdx=2πib1. Where b1is residue of fz.…

Q: Reverse the order of integratlon and then evaluate the Integral 10Tin6 Jinu! dx dy 9/10 et2

A:

Q: Evaluate the integral. dx dy dz O 168 84 O 252 O 28

A: The given integral is: ∫1e7∫1e6∫1e21xyzdx dy dz Let, I=∫1e7∫1e6∫1e21xyzdx dy dz

Q: Evaluate the integral Ja (2 – 2) " da, - by making the appropriate substitution: u =

A: The given integral is ∫x2x3-219dx

Q: Evaluate the integrals ∫8 cot4 t dt

A: The given indefinite integral is: ∫8 cot4t dt Since 8 is a constant, so take it outside. ∫8 cot4t…

Q: Consider the integral 7x – 21 da 2x – 3 If the integral is divergent, type an upper-case "D".…

A: the given integral is ∫027x-212x-3dx

Q: Use geometry and properties of integrals to evaluate

A: we have to  integrate the given integral ∫01(2x+1-x2+1)dx

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. '4 (x2…

A: Using the definition of integral.

Q: By using u = In x, evaluate the integrals In x dx.

A: ∫x-1xlnx dx Now put, u=lnx⇒dudx=1x⇒du=1x dx

Q: Evaluate the integral. 6x * de +C 17e -

A: The value of the given integral is 18x1/3 - 17ex + C

Q: Evaluate the integral. Scort 4x dx

A: To evaluate the given integral we will use various derivative and integration formulas as shown…

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: Use the Trapezoidal Rule to evaluate the integral S |r| x²dx O 2 O -2 O 1 -1

A: Given Intergral ∫-11xx2dx. We have to find the value of it by using the Trapezoidal Rule. The…

Q: z · 3°dz

A:

Q: Evaluate the integral: =°/1+ 64z*dz

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Q: Evaluate the integral by interpreting it in terms of areas. 3 + v9 - x2) dx

A: According to the given information it is required to interpret the integral in terms of area.

Q: rtoo Е. re dx स०२२

A:

Q: Evaluate the integrals in ∫3 sec2 t/6 + 3tant dt

A: Given integral is, ∫3sec2t6+3tant dt

Q: Evaluate the improper integral : 6be 8z" dx

A: Note: As per our guideline we are supposed to answer only one question. kindly repost the other…