b. I = S(1+ sin x)5 cos x dx

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: Use the indicated substitution to evaluate the integral.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) A) x cos(2x) dx B)e6θ sin(7θ) dθ

A: here we evaluate the integral      (A)   ∫ x cos (2x)dx     (B)  ∫ e6θ sin (70) dθ

Q: By reversing the order of integration, evaluate the following integral. [ f* x cos (y²) dy dx.

A: Given integral ∫03∫x29xcosy2dydx The objective is to evaluate the integral by reversing the order of…

Q: Evaluate the integral. (Use C for the constant of integration.) | 3x2 cos(mx) dx

A:

Q: use the indicated substitution to evaluate the integral.

A:

Q: I = S(1+ sin x)³ cos x dx

A:

Q: dx (b) J sin x· cos² x

A:

Q: Evaluate the integrals using the indicated substitutions.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

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

A:

Q: Change the order of integration and then evaluate the integral: ² x sin (x) dydx π/2 cx+1 1

A:

Q: S sin x e cosxdx

A: The objective of the question is evaluate the given indefinite integral using substitution method.

Q: Evaluate the following integral: (Note that the constant of integration has been added for you.) | =…

A:

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

A:

Q: Evaluate the integral. (Use C for the constant of integration.) s¯¹(x) dx COS

A:

Q: c) Evaluate the following Integration by parts for definite integrals. -5x dx хе 3 ii) . 2 Sin-dx i)…

A:

Q: Evaluate the following integrals (from A to E) A. Integration by parts cos dz i) (3t + t?) sin(2t)…

A:

Q: tan(x)dx, Ind: u = cos(z)

A: We have to calculate the given integral: ∫tan x dx We know the identity, tan x=sin xcos x Therefore,…

Q: how to solve problem in photo attached

A: Substitute x = t2 in the given integral and so the limit varies pi/2 to pi.

Q: Reverse the order of integration and then evaluate the integral. 5 5 sin y dy dx 0 x

A:

Q: Evaluate the following by changing the order of integration: 5 sin(y*) dy dx. 5x

A: First we change the order of integration and find limit of integration.

Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: Evaluate the given integral using the substitution (or method) indicated. (Use C for the constant of…

A: The integral is  ∫ ex/8 dx

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

A:

Q: Derive the formula by using integration by parts on the left-hand side. (Assume n > 0.)

A: Given:

Q: Evaluate the integral cos(x?) dæ dy by reversing the order of integration.

A:

Q: 2 sin? t sec“ t dt

A: To determine:

Q: dx 16. 2 2 x*Vx –16

A:

Q: Evaluate the integrals: A: So So x sin y dy dx

A: ∫0π∫0xx siny dy dx

Q: Evaluate the integral. (Use C for the constant of integration.) 4 sin Vx xp

A: To evaluate the given integral.

Q: Evaluate the given integral using the substitution (or method) indicated. (Use C for the constant of…

A: By using substitution we calculate the given integral.

Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin?(t) cos“(t) dt

A:

Q: Use the substitution technique to determine the following integrals:

A: Let,

Q: Reverse the order of integration and then evaluate. a. S S, x² sin(xy)dxdy

A:

Q: First make a substitution and then use integration byparts to evaluate the integral.   ∫Cos √x dx

A: Given: I=∫cosxdx for evaluating given integral, we substitute x=t…

Q: (1 – 3|x|) dx -2

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

Q: A/2 x+! I Į sin x dy dx -1 0 96.

A:

Q: Consider the following integral: sinx dxdy I By reversing the order of integration, the value ofI is…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) COS s-1(x) dx

A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

Q: Evaluate the integral 2 sin(x dy by reversing the order of integration. With order reversed, sin(x…

A:

Q: ∫dx/(sinx)(cos2x)

A: Integration is calculated using basic properties.

Q: 3n/4 cot a In(sin r) dx

A: Use integration by parts

Q: Apply the method of substitution to integrate the following integrals: dx I = ; a. Va²-x² b. I = [(1…

A:

Q: Evaluate the following by changing the order of integration: •3 sin(y?) dy dx. (6 marks)

A:

Q: Use the trapezoidal rule of integration to determine the value of the following integrals (a) | (2 –…

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: Find the integral for the following functions: - dx 1) . Vx²-2x+1 2) ſ e3se c(x), sec(x). tan(x) dx…

A: Solution: The objective is to find the value of given integral

Q: Evaluate the integral. (Use C for the constant of integration.) | 9t sin?(t) dt

A:

Q: Evaluate the integrals

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