1-X let dx , write the integral by using Beta function 0. 1 3 .a 2'4 1 B 2'2 .b O 3 .cO 2 2 1 B 4 2 .d .

Q: 3 Evaluate the integral c Ħ A) 1 B) 77 c) - Ť tan?xdx E)ユ-

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Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)´dx 2. S cos³ 3x dx 3. S tan5 2x dx

A: To evaluate the following integrals.1 ∫cos x+sin x2 dx2 ∫cos33x dx3 ∫tan52x dx

Q: Which among the following is an improper integral? -0.5 dx a. O5- -0.5 1-x2 csc?x b. Si dx V5-csc2x…

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Q: dx I = S е. a² +x²

A: The objective of the question is find the indefinite integral.

Q: Evaluate the integrals. -32 a. S x-6/5 dx 1 -π/³1 - cos 2x b. 2 -TT/3 -dx

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Q: 1. Evaluate the following integral: (1-e-²x) dx (a) analytically;

A: Note:- For this problem all the sub-parts  are different as methods are different. So, we can solve…

Q: 1- By using Gamma function , this integral I = z*e-?dz equal : a) 5i b) 24 c) 48 d) none of the…

A: Given : I=∫0∞z4e-zdz

Q: Evaluate the improper integral if it exists e'dx: 00 1 -1 0 e.2 O -e 3 O The improper integral…

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

Q: dx 4. Evaluate the integral 0<a <1. 1+asinx

A: According to question,Given integral,∫02π dx1+a sin x,where,0&lt;a&lt;1

Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: 15+0. The improper integral e* dx is

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Q: dx under Which of the following is the statement of the integral 1-Sinx-Cosx a suitable substitu…

A: the given integral is: ∫dx1-sinx-cosx we have to tell which statement is of the given integral under…

Q: 00 1 Evaluate the improper integral 1 dy dx as an iterated integral. x³y 2 e-X The value is

A: We apply first integration on y then on x

Q: Let b 2 4 be an integer. What is the result of the integral dx ? D) 0 E) 0 - 0o (the result of the…

A:

Q: A. Evaluate the following integrals. S(e* + 1)² dx 3.

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Q: B) Evaluate the following integrals: 1- dx 1-22

A: Let's find.

Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: For O S O 1/2 dx and using the substitution 1/2, the resulting integral takes the form: U=X U du -du…

A:

Q: 6. Evaluate any 5 of the following 6 integrals. (a) 12 dx 1 (b) (c) cos(50) de (e) [x²e² dr (d) (f)…

A: To evaluate the following integrals.d ∫xx+1 dxe ∫x2ex dxf ∫arcsin x dx

Q: following integrals 3 a) Evaluate IT2-4xy+4y² dxdy=? 0, 0.

A: Given that the double integral To find evaluate the double integral

Q: тх e COs nx dx

A: We have to evaluate the integral  ∫emx cos nx dx.

Q: Find the integral of ([sin(x)]^6){[cos(x)]^7)dx from x=0 to x = pi/2. 14/1001 15/2002 16/3003…

A: …

Q: e2x Evaluate the integral: dx 1 + eX

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Q: Evaluate the integral. integral  cos 3x e x dx

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Q: 2. When working out the integral below, with u, du method, S e sin2x cos2x dx (a) What is u = ????…

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Q: 1 dx. Evaluate the improper integral 2 e x(Inx)*

A: We have to evaluate the improper integral.

Q: 3. Evaluate the following integral using the Beta function: /2 sin 20 cos 40d0

A: According to the trigonometric identities sin2x=121-cos2x, cos2x=121+cos2x and…

Q: d) Determine the infinite integrals of the following e+2 i. ii. 2 3 sin2x dx

A: Evaluation of the integral

Q: iii. Find the particular integral (P.I) of y" + 9y = cos 3x

A: To find the particular integral P.I of  y''+9y=cos 3x

Q: Evaluate the improper integral if it exists e'dx: -0- e .2 O -e.3 O The improper integral diverges 4…

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

Q: 1. Evaluate the integral. S. a) t sin3tdt b) / V1+a* dx

A: (a) Given: ∫0πt sin 3t dt Apply integration By part : ∫I.II dx=I∫II dx-∫ddxI∫II dxdx Take: I=t and…

Q: a) Evaluate the following integrals 1) | xe3xdx x² sin x dx 3) | x sin 2x dx

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Q: dx 2. Find the integral x²(x+1) In (***) + C b. In (***) - +C 1+ C c. In (***) ++ c d. None of the…

A: Here we have to find the integral

Q: So 0 Evaluate the integral, if it exists. exc 1+e2x dx

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Q: II cos(s5) dt ds

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Q: Evaluate the improper integral: dx CA. 0 CB. -00 Oc. 0 CD. In 3 E. None of these

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Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: A. Evaluate the following integrals 1. So dx

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

Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

A:

Q: b) Evaluate each of the following integrals: 2 i) | cos(2x)dx, 4x3 -dx. 1+ x* ii)

A: Explained below

Q: Evaluate the improper integral if it exists e dx: -00 The improper integral diverges 1 0 e.2 0 -e .3…

A: The solution is given as

Q: •1-22 1-x 1. For the integral dV | dy dx dz , do the following. E a) Evaluate the integral.

A: Given ∫∫∫dV=∫01∫01-z2∫01-zdydxdz   E

Q: 1 -dx e +1 Evaluate the following integral: a >0

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Q: One of the correct steps to evaluate x2inx x²Inx dx to yield the correct integral A x?Inx B 1 x3 dx…

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Q: Find the integral of e*cos (x)dx

A: The given integral is:∫excosxdx.We will use integration by parts formula to evaluate the above…

Q: Sõlve the integral - In 3 x'e-*dx 2.

A: The given integral ∫0ln3x2e-xdx can be evaluated as, ∫x2e-xdx=x2×∫e-xdx-∫ddxx2×∫e-xdxdx+C…

Q: Find the integral of (1 + 2x)e^(-x) dx from x-0 to x--. A. 3 B. 4 C. 2 D. 1 O A B. DI

A: Use integration by parts for solving it,

Q: 2. Find the following indefinite integrals. (a) / sin(In(x)) xp (b) / º etan-(x) dx x2 + 1 sin(t)…

A: (a) ∫sinlnxxdx Let; lnx=t⇒1xdx=dt     =∫sint dt=cost+C put again: t=lnx =coslnx+C Result:…

Q: 5. Calculate the following integrals. (a) / (b) / (c) / sin x cos x dx x sin(x? + 5) dx 3 el/x dx x2…

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Q: Answer 1 only. Upvote if it is typewritten.

A: We have to find the integral