p* sin o cos o dp dộ dê

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: Taking substitution

Q: Transform the integral fo o sin o sin 0 do de by the substitution x = sin o cos 0, y = sin ø sin 0…

A: Solution: The given integral is I=∫0π2∫0π2sinϕsinθdϕdθ The substitution is x=sinϕcosθ, and…

Q: Evaluate the integral S ( Inti+ 3t' sin (t) i+ k) dt.

A: We apply integration separately to each term and then simplify

Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

Q: Evaluate the integrals

A:

Q: The integral TT tan x sec?x dx 2 O none of them is an impróper integral of type I that diverges is…

A: Improper integral

Q: cOsy du dy

A: Definition used-    Double integral -                             ∫ab∫cdg(y)f(x)dxdy…

Q: Evaluate the fo llowing integrals S Sin () dx

A:

Q: evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a.

A:

Q: Evaluate the integral by making the given substitution.

A:

Q: Evaluate the iterated integral: a " cos(2) dy dar.

A: The iterated integral is given as:…

Q: Use contour integration to compute the following integrals. (a) 1. 2π cos(20) dv 5+4 cos v

A: (a) Given integral ∫02πcos(2ϑ)dϑ5+4cosϑ. The objective is to compute the integral by using contour…

Q: Evaluate the iterated integral. z sin(x) dy dz dx

A:

Q: Je t ež cos (2t)dt

A:

Q: dw V5 – e-2

A:

Q: evaluate the iterated integral.

A: ∫12∫042xydydx

Q: Evaluate the integrals in ∫esec πt sec πt tan πt dt

A: Given: ∫esecπtsecπttanπtdt for evaluating this integral we substitute esecπt=u now differentiating…

Q: Evaluate the integral using the given substitution. 15) 1- sin cos dt, u = 1 - sin 13 1 - sin + C A)…

A:

Q: Evaluate the integral using the given substitution. Sx cos (10n2) dx, u = 10x² sin (10x²) - C sin…

A:

Q: Evaluate the given iterated integral by reiterating it in a given order ex'dy dx dz = dz dy dx Z.

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: Evaluate the integral. S (sec r- sin r) dx

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Evaluate the integral in terms of u. sinh u• du = + C %3D 3.

A:

Q: Compute the following integrals. (a) tan (x) sec°(x) dr. (b) sin (x) tan(x) dx. 2.

A: We have to find the following integral

Q: Evaluate the integrals:

A: Integration: ∫sect dt=ln|sec t +tan t|+c∫u.v dx=u.∫v dx -∫[ddx(u).∫v dx]dx   [ by parts]

Q: Transform the integral fo So sin o ne do de by the substitution x = sin o cos 0, y = sin o sin 0 and…

A: The given integral is, ∫0π2∫0π2sinϕsinθ dϕdθ To substitute x=sinϕ cosθ  and  y=sinϕ sinθ The limits…

Q: Express the integral in terms of the variable u, but do not evaluate it. In x dx; u = Inr In a ) du

A:

Q: Evaluate the integral b. 0 (z sin x + z cos y)dzdydx

A:

Q: Evaluate the definite integral. 2exin ( z ) cos(z)dz 0.

A:

Q: SJcos (In x) dx Evaluate the integral

A:

Q: Evaluate the integral using the given substitution. 5- sin cos dt, u= 5- sin- cos 1 O A. 5- sin 3 t…

A:

Q: Evaluate the integral using the given substitution. Jx cos (5x?) dx, u=5x? O A. sin (5x2) +c 1 O B.…

A: Note:Since you have asked multiple question, as per our guidelines we are supposed to answer only…

Q: Evaluate the iterated integral. 5 (T/2 r cos e dr de dz

A:

Q: Evaluate the integral. re 8 In(x) dx NOTE: Enter the exact answer.

A:

Q: Evaluate the iterated integral. TT/2 (10 cos(e) r dr de of

A: ∫0π2∫010cosθrdrdθLet∫010cosθrdr=[r22]010cosθ∫010cosθrdr=[(10cosθ)22-0]∫010cosθrdr=[100cos2θ2]Therefo…

Q: evaluate the integral in the form a sin(u(x)) + C for an appropriate choice of u(x) and constant a.

A:

Q: 2. Evaluate the integral by interpreting it in terms of areas: J | sin x dx. -T

A:

Q: Evaluate the integral. "π/4 J.T tan (0) sec²(0) de

A: This question can be solved using integration by substitution.

Q: Use a double integral to find the area of the shaded region. 1/2 10 r= 5+5 cos e -5 5 10 -10

A: The integral of a function is with respect to two different variables, so if f is a function of two…

Q: Evaluate the integral using property of So √x e² dx' the F

A: Given:  To evaluate ∫x1/2*e-2xdx using property of pdf ?

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A:

Q: Evaluate the integral: T So sin(x)dx

A:

Q: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

Q: Evaluate the integral using the given substitu Sxcos (5x?) dx, u=5x? dx, u= 5x sin (5x?) +c О в. sin…

A:

Q: z · 3°dz

A:

Q: (e2x –1)2 dx 1. e 2x

A:

Q: Use a double integral to find the area of one loop of the rose r = 2 cos(30).

A:

Q: Which of the following integrals represent the area enclosed by the smaller loop of r = 1 +2 sin 0?

A:

Q: Set up the integral for the common interior of r1 and r2.  r1 = 3 + 3 cos theta  r2 = 3 sin theta

A:

Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given