Evaluate the definite integral. n/4 sin(t) dt cos²(t) COS

Q: Find the following definite integrals using an appropriate substitution. (a) /2 cos a sin(sin x) dx.…

A: a) The given integral is ∫0π2cos(x)sin(sinx)dx. Evaluate the integral as follows. Apply u…

Q: Q:: Find the integral for the following functions: - 1) S sec x. esec x cos²x

A: To find the integration (secx×esecx/cos²x)dx

Q: Evaluate the definite integral. cos(T2) dz sin 8n Answer:

A: The given integral:∫08cosπxdxWe need to evaluate the above integral.

Q: Evaluate the following integrals: 1.5 cos'x dx sin³x sec*x dx tan³x 2. 3. sin?x cos?x dx 4. cos (3x)…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 71. Perform the following definite integral. 2 (1 – e-x/2) dx x=0

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: 5. Evaluate the integral. e cos 0 sin 0 de

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Q: Determine the following definite integrals: (a) (sin(x) + =) d.x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: If fex) x2 f'co) 19+ t? dt find f'c3) %3D

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Q: |-e+2 COS X 3 x- Sin x

A: Let,

Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

Q: Evaluate the definite integral. 4 cos(πt/2) dt

A:

Q: Evaluate the definite integral. 7 cos(xt/2) dt

A:

Q: 4. Find the following indefinite integrals: 6 sin(x) cos(x) (a) S sin? (x) + 1 dæ;

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Q: Evaluate the definite integral (cos(t), sin(t))dt

A:

Q: Use the value of the first integral I to evaluate the two given integrals.

A: Given: I=∫0π2cosθ-2sinθdθ=-1 we know that ∫abfxdx=-∫bafxdx

Q: 1. Evaluate the following definite and indefinite integrals. a) St sec2(t?) tan*(t²) dt

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL  BE ANSWERING ONLY THE FIRST…

Q: Evaluate the definite integral 2 (sin t, cos t) dt. COS 7/2 Select the correct anSwer helow:

A: We have to find out

Q: Evaluate the definite integral. -7/6 sin(t) dt cos?(t) COS

A: We have to evaluate the definite integral…

Q: (g) et +1 dx (n) dx 2 sin“ x

A:

Q: 3)Find the indefinite integral. S713 sin(t') dt

A:

Q: Which of the following is one of the correct steps to evaluate | cos'x dx to obtain the desired…

A: Solution :∫cos7xdx∫cos6xcosxdx∫cos2x3cosxdx∫1-sin2x3cosxdx

Q: Find the value of the integral e* cos x dx Select one: a4 n4 .2

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

Q: Q1/ Evaluate the following integrals: (a) / sin' cos를 dx. (b) S dx . (e) Sr² G- 1) dr .

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

Q: Evaluate the definite integral. Tt/2 cos(t) dt 31 + sin(t)

A: Solve the intregal

Q: Evaluate the given integral. ∫ (e2x cos x -2e2x sin x)dx.

A:

Q: 6. Evaluate the following definite integral using the fact that sin x dx = 1. S. | (2 sin x + 3) dx

A: ∫0π2(2sinx+3)dx Take integral for each term ∫0π2(2sinx+3)dx∫0π22sinx dx+∫0π23 dx2∫0π2sinxdx+3∫0π2dx…

Q: Using an appropriate substitution, the integral cos cos (ln(2x)) X is equal to dx - — cos(ln(2x)) +…

A:

Q: 7/2 S/² sin(x/2) cos(x/3) dx

A: This question is based on definite integral.

Q: TT 1 dx 1+ 2 sin? x

A:

Q: 4. Evaluate the following indefinite integrals. (a) / (cos(0) – sec(0) tan(0)) d0

A: Explanation of the answer is as follows

Q: * T14 Evaluate the definite integral: a sin? 4x cos² 2x dx T/16 O T/8 O T14 t/32

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Q: Evaluate the following definite and indefinite integrals. (a) / sin(x) cos(x)ešin(=) dx (b) L. V5/2…

A:

Q: Evaluate the definite integral on the interval [0, pi/4] sin(t) / cos^2(t)  dt

A: By substitution, we calculate the value of given integral.

Q: Find the definite integral of: * 27 cos -w ) sin w) dw. O - 1/2 O - 1/12 О 12 2

A: The given integral is ∫π2π cos3w2 sin5w2 dw. Evaluate the above integral as follows.

Q: Find the indefinite integral. х cos 9пх2 dx

A:

Q: Evaluate the definite integral. cos(xx) dx

A: We have to evaluate the integral                                                      ∫03cosπxdx

Q: Evaluate the definite integral. *a/6_sin(t) _ dt cos?(t)

A: Given, ∫0π6sintcos2tdt  We have to evaluate the definite integral.

Q: Evaluate the definite integral. 7 cos(t/2) dt

A:

Q: Solve the following integral dx (1) S; 2+cos x

A:

Q: T/° cos® 3 0de Co.

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Q: Evaluate the following indefinite integral | 10 sin(x) – 2 cos(x) dx = +C

A:

Q: sin 3x cos 5x dx

A: ∫0π/8sin3xcos5xdx here we use formula  sinacosb = (1/2)[sin(a+b) +sin(a-b)]

Q: Evaluate the indefinite integral sinr cos rdr 3 + C

A:

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: Evaluate the definite integral of the following: a. ∫0π/2 cos(2x/3) dx Read as: The integral of…

A:

Q: (7) Evaluate the definite integral. | sin?t cos tdt

A:

Q: cos“(x) sin(x)dx

A: See attached file for a step by step explanation to find the given integral.