Evaluate the following integrals, where the coefficients 4,B,C, are the last three digits of your index number(0,2,8):- i) By= [(4x sin( y°z?) + -Ce"* )ôx By= [(4x° sin( y²=³) + Bv* -Ce** )ây ii) By iii) S(4x° sin( y²=*) +- - Ce= )ôz

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

A:

Q: Evaluate the indefinite integral; f Vtan 3x sec2 3x dx OA)-(2(tan [3x)^(3/2) ] /9 + C OB) I DON'T…

A:

Q: 3 sin 3 ycos ydy

A:

Q: evaluate the indefinite integral

A: The given integral is

Q: Evaluate the definite integral. 4 dz V7z +8

A: Using definite integral

Q: Csin $ 3 y cos*3 ychy

A:

Q: 5tan 2x -dx sin²2x-1 8.

A: Put tan2x=t and using integration of ax dx =ax /loga

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

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

Q: Use integration by parts to evaluate the integral: sin(In(9x))dx 1 x(sin (In)(9æ))– cos(In (9x)) + C…

A:

Q: Evaluate the integrals

A:

Q: Calculate the integral of y = 11 cos (8x) from 0 to Answer = Number Leave your answer in exact form…

A: on solving this we get the

Q: What substitutions are made to evaluate integrals of sin mx sin nx, sin mx cos nx, and cos mx cos…

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 following integrals, where the coefficients 4,B.C, are the last three digits of your…

A: First will be right answer.

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

A:

Q: evaluate the integral fromn 0 to pi/2 (cosx)^3

A:

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫ cos (2x +…

A: ∫cos2x+5 dx Now put 2x+5=u Differentiating with respect to x, we get 21+0=dudx⇒2 dx=du⇒dx=du2

Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: 3. Evaluate the integrals √tanh x sech² xdx

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 integrals ∫sin 2θ - cos 2θ/(sin 2θ + cos 2θ)3 dθ

A: We have to evaluate the integrals: ∫sin2θ-cos2θsin2θ+cos2θ3dθ This integration will be solve d by…

Q: 10) Evaluate the integrals by substitution 2 -dxp 3 -2 (x² + 2)° a)

A: We have to evaluate the integrals by substitution method: ∫-22xx2+23dx Assuming, t=x2+3 Then…

Q: Find the indefinite integral (10tan?x+ 16)dx, а. 10tanx + бх + C 10 3 b. -tan'x+16x +C 3 10 3 tan'x…

A:

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

A: GRAPH

Q: Identify which among the numbers are odd-numbered integrals. 1. S21 cos 7x dx 2. S csc* dx 14. S dy…

A:

Q: evaluate the integral (Usec. af nitegratun) for the constant बदेशव 1ehan) 5x cos (8x) dx

A: Given

Q: Evaluate the definite integrals S(2sin(x)-3cos(x)dx

A:

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

A:

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

A:

Q: de 2/2 V5 9 18

A: Solution: Here let I=∫dxx29-x2 Substitute: x=3sinu u=sin-1x3 and dx=3cosudu Thus,…

Q: Evaluate the integrals ∫cos 3x cos 4x dx

A: Evaluate ∫ cos 3xcos 4xdx

Q: Show detailed solution for the following integral: (Non-anonymous questionO) S tan'z sec³z dz 7

A:

Q: Evaluate the indefinite integral: (3e" + 6 sec? u) du: |+ C.

A: As per guide line we have

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

A: Given:-                 To prove the result concerning iterated integrals that…

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: You found that the reduction formula of a certain integral is In = a" sin 2x + nx"-1 cos 2x – n (n –…

A:

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

A:

Q: 1 Scos 3x sin* 3x dx 1.

A:

Q: To evaluate the integral dz, we use Select one: Substitution with z = 2 sin 0, where 2 O…

A:

Q: Evaluate the indefinite integrals by using the given substitutions to reduce the integrals to…

A: SOLUTION-

Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

A:

Q: Evaluate the following indefinite integrals. 1 4x + Vx + dx ,3 (a) -

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 5 Only one of these calculations is correct to evaluate the definite integral x² In(x) dx 1 Using…

A: First we have to find h and it's corresponding formula.

Q: Only one of these calculations is correct to evaluate the definite integral Vx+1 dx Using the…

A:

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

A: Given∫123x-5dx

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…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.