Integrate the following integrals using either integration by parts or integration by substitution. Se-20 sin 60 d0

Q: 1 dx х6—х

A: To evaluate the integral: ∫1x6-xdx Solution: ∫1x6-xdx On simplifying further we get:…

Q: e2x sin 2x dx

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Q: Use the table of integrals at the back of the text to evaluate the integrals ∫sin t/3 sin t/6 dt

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Q: Evaluate the following integrals using integration by -parts S sin-1 y dy

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: sec(2x) tan(2.x)dx

A: We will find out the required value.

Q: Evaluate the following integrals i. SxIn(x+1)dx sin (Inx)cos (Inx), 2 ii.

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Q: Find the following indefinite integral. Use C for the constant of integration. VI + 3 V) dx Answer

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Q: (x² + 2x) cos(2x) dx

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Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: I = S(1+ sin x)³ cos x dx

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Q: Use a substitution to change the integral into one found in the table of integrals, then evaluate:…

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Q: sin(6x) Vi? +4 dt 7

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Q: Evaluate the integral by making a u-substitution and then integrating by parts. NOTE: Enter the…

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Q: Use the integration by parts to evaluate the following integral by assuming u = COS 2 dx (cos a + a…

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Q: Evaluate the integral by substitution a) "x sin(x?) dx

A: Given : ∫0πxsinx2dx

Q: Evaluate the following indefinite integrals using integration by trigonometric substitution.…

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Q: Evaluate the following integrals TC 2x a) -e + sin dx V3x 0. 3. cot(-2x) csc?(-2x) dx b) 7.

A: (a) I=∫0π53x-e+sin-2x3dx =∫0π53x dx-e∫0πdx+∫0πsin-2x3 dx  ∵∫(u+v) dx=∫u dx+∫v dx…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: To evaluate the integral by making the given substitution

Q: Use the Table of Integrals to evaluate the integral. e70 sin 60 de

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Q: Evaluate the following integrals S, sin () cos" () dx ) dx

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Q: Evaluate the following integral by changing the order of integration. I | cos(x*) dx dy

A: We have to evaluate the integral by changing of order.…

Q: - sec (r)) de 3a sin(r+5) da

A: Integrate

Q: Evaluate the following integrals using integration by parts | sin-l y dy sin 2x dx

A: To determine the indefinite integrals.

Q: c) Seax.Sinbx. dx =? Calculate the integral

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Q: Calculate the following integrals. I (b) /2 I sec rdx-

A: The given integration is  I = ∫xsec2xdx

Q: Find the integral for the following : dx 2- fe-*sec? (ne-*)dx 3- Sdx ZVI+2x 1+e*

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Q: sin x cos? x dx

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Q: Approximate the following integrals using the Trapezoidal rule. 0.5 b. dx d. re dx

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 2 sin? t sec“ t dt

A: To determine:

Q: Find the values of the following Integrals: ii) S sinx tan'ccord dx ü) Sex uci+ e* ) dze in) St…

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Q: Integrate the following integrals using either integration by parts or integration by substitution.…

A: The given integral is ∫xsin1+x32dx. Take u=x.  Then, du=12xdx⇒du=12udx⇒dx=2udu Note that,…

Q: dx 16. 2 2 x*Vx –16

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Q: Use integration by parts to evaluate the integral.

A: Apply integration by parts,

Q: Evaluate the following integrals. 4 (a) (cot? 0 + csc? 0 sin 20) d0

A: definate integration

Q: |/ (cos(x) + sin(x))² dx

A: *Used the (a+b)2= a2 + 2ab + b2 formula.

Q: By using a trigonometric substitution x = 3sece ,where 0 s0 < 27 "he integral 3 Vx² - 9 dx can be…

A: We have to choose the correct answer from the given option according to the given condition

Q: Evaluate the following integrals using Integration of Hyperbolic Functions. 14. S sech? ( Inx) dx…

A: Integration is the inverse of differentiation and we are going to use that concept here. Therefore…

Q: 16. | (ez/a – e-xla)dx. n/3 sec 0 tan 0 do. Vesec e 17.

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Q: 18. | V4 - х? dx

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Q: 1. sin Va +1 dx

A: The integral function is ∫sin3x+1dx

Q: Evaluate the following integrals using the tabular method. (i) 2x sin 2x dx

A: We need to evaluate the integral ∫e2xsin(2x)dx by tabular method

Q: Solve the following integrals: i. S(e**sin(2x))dx using integration by parts or tabular meth

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Q: Consider the following. 4,000e0.1X dx Find a substitution to rewrite the integrand as 40,000e" u =…

A: The given integral is- ∫4000e0.1xdx Let u=0.1x Differentiating w.r.t. x to both sides-…

Q: Find approximate value of the following integral by using the trapezoidal rul 10 " 10 sin(20x²)dx…

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Q: arctan(3r) da =

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Q: Consider the following. 9,000e0.1x dx Find a substitution to rewrite the integrand as 90,000e" du. u…

A: To evaluate I=∫9000e0.1xdx Substitute u=0.1xdu=0.1 dx

Q: Evaluate the integral. (Use C for the constant of integration.) cos (@). 4 da V sin(a)

A: Here we evaluate the integral∫4 cos5(α)sin(α)dα

Q: Solve The following integrations using Trigono metric indegrals XP S cos?ex sin"2ndx cos'ex

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Q: Evaluate the integrals

A: We have to evaluate the definite integral: ∫-ππ1-cos2 t32dt We know the trigonometric identity, cos2…