4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

Q: Evaluate the integral. 17) S sin (3x - 2) dx

A: From the given problem:   I=∫ sin3x-2dx..(1)   Let,   u=3x-2   Now differentiate with respect to x:…

Q: 3 sin 3 ycos ydy

A:

Q: evaluate the indefinite integral

A: The given integral is

Q: 3 Which of the following is equal to sec ² x tan³x dx to obtain the correct indef inite integral?

A:

Q: In evaluating sin (2x) cos(2x) dx by substitution, if u = sin( 2x) then what will be the resulting…

A: We have to calculate integral by substitutions

Q: Evaluate the integral: integral from 0 to Pi/2 of cos^3(x)*sin^(2/3)(x)dx

A:

Q: In evaluating / * sin3(2x) cos(2x) dx by substitution, if u = sin( 2x) then what will be the…

A:

Q: Evaluate the integral. 4tm 2 sin(2t) dt

A:

Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Csin $ 3 y cos*3 ychy

A:

Q: Evaluate the integrals

A:

Q: 1 use this fact and the properties of definite integrals to evaluate 3 (7 - 6х2) dx. Given that x²…

A:

Q: Use reduction formulas to evaluate the integrals ∫ 8 cos4 2πt dt

A: To solve,    ∫ 8 cos4 2πt dt Using reduction formula.

Q: Obtain a formula that expresses the integral ∫cosn x dx

A:

Q: Evaluate the integral: CT/2 cos² (4x) sin³ (4x) dx.

A:

Q: Evaluate the integral.  integral  cos 2 x tan 3 x  dx

A:

Q: Evaluate the integral from -n/2 to +t/2 of x² sin x.

A: Given integral

Q: Evaluate the integrals.∫cos 3t / (1 + sin 3t)dt

A:

Q: Evaluate the integrals. ∫sin 2x/(1 + cos2 x)dx(Hint: sin 2x = 2 sin x cos x.)

A: We have to evaluate ∫sin2x1+cos2xdx We know that sin2x=2sinxcosx So, the given integral can be…

Q: Evaluate the integrals sin2.x -dp- J(5 + cos2.x) e) 3

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

Q: Evaluate the integral: 2 So sin(4t - u) du dt

A:

Q: What is the integral of sin^5 x dx if the lower limit is O and the upper limit is T/2?

A: We have to find out

Q: Evaluate the integral.  integral  cos 2 x sin 2x  dx

A: Given integral to evaluate  ∫cos2xsin2xdx substitute sin2x=2sinxcosx ∫cos2xsin2xdx=∫cos2x2sinxcosxdx…

Q: Evaluate the integral of sin^6 x dx from 0 to T/2.

A:

Q: Evaluate the integral. integral  cos 3x  sin 2x dx

A:

Q: 5) Evaluate the integrals using appropriate substitutions a) sec 2x tan 2x dx b) 2x+1

A: Given that, a) ∫sec32x tan 2x dx b) ∫x2x+1dx For evaluating those indefinite integrals,  we need to…

Q: Evaluate the indefinite integral: 3 dx J x In(5x)

A:

Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

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: set up an integral ....bounds x=3pi/4 x=-pi/4 y=-sinx and y=-cosx

A: GRAPH

Q: 2 Which of the following integrals is equal to (3x – 5) dx if u=3x – 7?

A:

Q: compute the definite integral.

A:

Q: Evaluate the integral 10 cos(In(x)) dx, x > 0

A:

Q: Evaluate the integrals: 1. ftan5 x dx 2. f sin 2x cos 3x dx

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

Q: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

A:

Q: de 1 + sin 0

A:

Q: Evaluate the integrals ∫cos t/1 - sin t dt

A: Given :           ∫cos t1-sin tdt

Q: Compute the Improper Integral by Using the Residue +00 x sin x (x2 + 1)2 dx

A:

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

A:

Q: Evaluate the integrals in 1 1. Vx(1 + x) sin x sec x dx

A:

Q: Evaluate the integral ( sin(In(2+2x)) x+1 dx

A: Given: ∫sinln2+2xx+1dx

Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: Evaluate the integral: 2² sin (²) dt du

A: To evaluate the integral: ∫π2π∫0u2sintudt du

Q: 3- Evaluate the integral sin(In x)dx

A: We have to use integration by parts 2 times here.

Q: 2 Which of the following integrals is equal to (3x – 5) dx if u =3x – 7?

A: Given∫123x-5dx

Q: Evaluate the integral: ( ) sect tan ti +tcos 2t j+sin² 2t cos 2tk 1k)dt

A: the given integral is: ∫0π4sect tant i^ +t cos2t j^ +sin22t cos2t k^ dt we have to evaluate the…

Q: 1. Evaluate the iterated integrals. √27x² (a) [sin - dydx (b) √√x² - y² dydx

A:

Q: Evaluate the integrals ∫8 sin4 y cos2 y dy

A: the given integral is: ∫8 sin4y cos2y dy we have to evaluate the given integral.   let the given…

Q: In x dx

A: To Solve for the integral