| cos xdx sin x

Q: find the area bounded by the given curves.

A: Given curves are  y=2sinx and y=sin(2x) , x lies in 0 to pi The curve y= 2sinx is above the curve…

Q: y = Cje" cos 3x + C2e2 sin 3x %3D

A: Given,      y=C1e2x cos 3x +C2e2x sin 3x

Q: 2 sin (t) cos (t)d J

A:

Q: cos z dz (4 + sin z)?

A: The solution of above integral is written in below steps.

Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0) %3D

A: Separation of variables.

Q: sin xdx 3 S cos° x

A:

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 - y³)żdy

A: Given integral ∫b2y6-y812dy The objective is to evaluate the integral by trigonometric substitution.

Q: dx Integrate by trigonometric substitution: .2 4x² -9 2

A: Given integral :

Q: Find all x and y between O and 27 so that the equation is true. cosx+i siny = sinx+i x = 4 or 4y = 2…

A: Explanation of the answer is as follows

Q: J, sin a sin? cos" ,dx COS 2 2 2.

A:

Q: If V = x² + y² where, x = a cos t, y= b sin t, find AP and verify the result. dt

A: x=acost y=bsint V=x2+y2 put the values of x and y V=acost2+bsint2 V=a2cos2t+b2sin2t

Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

A:

Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

A:

Q: Evaluate the integral (Trigonometric Substitution) x*dx J (x² + 4)² 2

A:

Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: Reduce to first order and solve 1> 2xy"= 3y' Cos n ii) xy"+ 2y'+zy = 0, Y, = ニ

A:

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A:

Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: Use the equations to find dz/əx and əz/ðy. хуz %3D sin(x +у + 2) əz ax əz ду II II

A: We have to find partial derivative.

Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

A:

Q: 3. ® Find the genelal Solution of the differentral egation (D'+ 25) y = cscX Sinx t Sin 5X cos 3X

A:

Q: Use Green's Theorem to evaluate |(3ye2* – 7 sin? (3x* )) dx +(5x* +2x’y² +8e*-1y+2 where C is the…

A:

Q: .2 x cos?y dx + tan y dy = 0

A: The given differential equation is  x cos2y dx+tan y dy=0 Solving the the given differential…

Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

A:

Q: The equation (tan?x+3y?) sec?xdx+(3tan?x+y²)dy=D0 can be solved by A Bernoulli's Equation DE with…

A:

Q: T/2 COS z xp V4 - sin? a

A: givenI=∫0π2cosx4-sin2xdxsubstitute  sinx=t therefore limits will change t=sinπ2=1  to t=sin0=0after…

Q: Obtain the integrating factor of the non-exact DE, (2 + ycosx)dx + xcosxdy = 0. a. secx b. cosx c…

A: Integrating factor

Q: dr = b (cos(O)dr + r sin(O)dO)

A: Given dr = bcosθ dr+rsinθ dθdr(1-bcosθ) = rsinθ dθdrr = sinθ dθ1-bcosθintegrate on both sides to get…

Q: Find all intersection points between r = –sin 0 and r = v = V3 cos e.

A:

Q: Evaluate the integral. 1/2 cos(t) dt 1 + sin?(t)

A:

Q: The complex integral J(tan 2rz) dz is,

A: Introduction :

Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

A:

Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

A:

Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: Evaluate the iterated integral. cos(e) 3r2 sin(e) dr de

A: Given query is to find the value of the integral.

Q: (a) Calculate and fully simplify |a° cos(x) dzr. Hint: Considering a mnemonic for integration by…

A: Note- Multiple questions are asked, I am answering the first question. Please repost for other.

Q: Use the substitution formula to evaluate the integra 2. 3 cos xsin x dx 1/3 OA. 8. O B. -0.126 %3D…

A:

Q: Find / cos (z + y)dA where D = {(x, y) | 16 < z² + y² < 36} COS

A:

Q: evaluate using Integration by Parts, substitution, or both if necessary.

A:

Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: Integrate f,-¿ S=; cos x²dx dy =1 (x= 1 y=0 Jx=y Select one: a. cos1 b. .5cos1 C. sin1 d. Non of…

A: We will find out the required value of given integral.

Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: Find the length of the cardioid r = 1 – cos 0.

A:

Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: E valuate:- seč (cosx) dXdy Sinly

A: We will have to evaluate: ∫01∫sin-1yπ/2sec2(cosx)dxdy.

Q: dx If x² – 2x – 4 is solved by trigonometric substitution, the resulting integrand is?

A: The integral function is ∫dxx2-2x-4dx

Q: J 1 (x) =, cos X 0 صواب ihi O

A:

Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

A: