O! Find tue indefinite integrel by q meleing tue febstelion d=4 Sin o. 2 *7 16-x"

Q: The Lineo Differ ential Eguatios of Order n in ope-ator form Find F(D)= Dx~4Dx +3 when u = 3x² + 2…

A:

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: me result of the integral in 0 given | V ²– 25 -dy is 5 tane – 50 +C , y A) True B) False

A:

Q: Evaluate the integral n²/4 cos vt dt Vt sin I Jesin vE n²/36

A:

Q: O Calculate He in tegual usng the Caucly Integral Theoren sin b (2) dz

A:

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

A: The iterated integral is given as:…

Q: 5. Evaluate triple integral Szr? sin e dz dr d0.

A: We know that,∫sinxdx=-cosx∫xndx=xn+1n+1The given integral…

Q: Evaluate the iterated integral. 1 1I 11ze- dx dy dz O Jo Jo

A:

Q: Evaluate the integral. (2 + 2y)? dy

A:

Q: sec(2) tan(z) – 1 dz 1 dz

A:

Q: consider limaçon r = 2 + 3 cos θ and the circle r = 2 cos θ in one polar plane.   - Set up the…

A: Plot the curves for the given limacon and the circle. The shaded region represents the area inside…

Q: Supply the missing integrand and the limits of integration n/2 2sin e r cos?e dr de = | _de 2sin e…

A:

Q: The value of the integral (17 tan z- 17 sec r)dr = %3D O -68 O 4 O 68 O-4

A:

Q: Integrate f(z) = 6 tan(z²) counterclockwise around the unit circle, using Cauchy's integral theorem…

A:

Q: 5. Find the total area between r = 4 sin(0) andr = 7 sin(40). %3D %3D

A:

Q: Which substitution is needed to evaluate the integral S tan* x sec² x dx =? u = tan* x, du = sec? x…

A:

Q: evaluate the triple iterated integral.

A:

Q: 22 + 1 dz 22(2z + 3) K

A:

Q: · sinxdx Jo 1+cosx -t integralinde . x = 15 - O A) Jo 1tcost sintdt B) ("/2 costdt 1+sint costdt OC)…

A:

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

A:

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: m, nEN imperding cosM X sin x tor Integral obtain re duction formula. u sing this Calalate integrol.…

A: Topic : integration

Q: Evaluate double integral 0 to 2, x to 2 2y^2 sinxy dydx

A: We have to integrate the double integral:

Q: Evaluate the integral. | (1+5e tane) sec?e de sec 0 de 4 | (1+5e (1+5 e tan e sec 0 de = (Type an…

A:

Q: Evaluate integral 8 to 2 (4x + 3) dx in two ways:(a) Using area and geometry.(b) Using the…

A: Given:

Q: Evaluate the integral ² ² sin² 20 r dr de where D = {(r, 0)| 0 ≤ 0 ≤ñ, 0≤ r ≤ 2√cos 20}. X

A: Solution: ∫∫Dr2sin2(2θ)rdrdθθ→0 to πr→0 to 2cos 2θ

Q: J sin (In ev) de

A:

Q: Evaluate the following integral JI (1 – (x + y))dA where T is the triangle with vertices (0, 0), (1,…

A:

Q: ce³ dr dy dz.

A: Given integral is I=∫01∫0z∫20yze-y2dx dy dz First we integrate it with respect to x. I=∫01∫0z∫0ydx…

Q: Evaluate the triple iterated integral. 12 2 3. xyz dx dy dz

A: Given a function f(x,y,z)=xyz3 To find ∫02∫02∫-12xyz3dxdydz

Q: Q5. Usung Maclaurin's thcorem expand, 5tanx as þar as +he term containing x". QC. Prove that , sinx…

A: A Maclaurin series is given by f(x) = ∑k=0∞fk(0)k !xk Given function f(x) = x5 tan x     Here, each…

Q: Evaluate the integrals

A: Given information: ∫0π34sinucos2udu

Q: Find the area inside r = 2(cos 20- sin 2 0) and outside r 1 %3D

A: The area inside r2=2(cos2θ-sin2θ) and outside r=1 is:

Q: Evaluate the triple iterated integral. 2 2 2 xyz dx dy dz of Jo

A: Given that ∫02∫02∫-12xyz5 dxdydz

Q: 3 3y Evaluate the iterated integral ry de dy.

A:

Q: pts Evalaute the integral y sin(z) dz dy dz. Enter an exact answer using fractions and radicals as…

A:

Q: Consider the following. dz 4z + 2 1 Find a substitution to rewrite the integrand as du. 4u du = dz

A: Given : ∫dz4z + 2

Q: Evaluate the integral. cos y dy sin'y +2 sin y - 15 2. cos y dy 2. siny +2 sin y - 15 (Type an exact…

A:

Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: save the g0llowing intial verlue problem dr-x Sin スe, rl)=3 de rz? type as eyact anwse Using I as…

A:

Q: Evaluate the triple iterated integral. T/2 r cos é dr de dz Jo

A:

Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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: The suitable substitution to evaluate the integral cot (2x) dx is sin (2x) O u= tan(2x) O u= csc(2x)…

A: Integral is given

Q: Determine a definite integral that represents the arc length of r = 2 cos(0), 0 < 0 < do

A:

Q: Prove that tan'z= leto 1/2 in (1+2) tan't z • tanw=Z Z = Sinw cosw

A:

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

A:

Q: In Evaluate the integral: Sto st² sin s teu du ds dt

A: The given integral is: I=∫12∫tt2∫0lnsteududsdt   The Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: 5. Find the total area betweenr = 4 sin(0) andr = 7 sin(40). %3D %3D

A: