(a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using substitution method.

Q: dx Perform the Integrations 1+ sin x+ cos x

A:

Q: Calculate integration | cos -1 1 dx

A:

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: Solve d²y dx² - cot x dy-sin² x.y = cos x - cos³ x. 2 dx

A:

Q: Can you help me step by step?

A: The given function is,

Q: Evaluate / x cos(128x)dx. Use capital C for your constant of integration.

A:

Q: - $x² cos(x³) dx

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Let D be the differential operator ddx, we have t find function f such that  fDgx=0, where…

Q: Sx-3) (sin (In x) + cos (In x)} dx equals

A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

Q: (b) Use integration by part or tabular method to find i. 2e2" cos 3x dx. ii. x° sin 3x dx.

A:

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

A:

Q: Evaluate f x² cos 4x dx Evaluateſ sin* 3x cos3 3x dx Evaluate the integral J x²+x-1 dx x(x²-1)

A: Given:   i) ∫x2cos 4x dx      integrate by parts ∫fg'=fg-∫f'g     here f=x2,f'=2x , g'=cos…

Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: Find dy/dx using implicit differentiation a. siny2+cosx2=1 b. y+x2+e3xy2=y2

A:

Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: 2- X %3D +2 3- Coshx dy +(y sinh x+e) dxo 36

A:

Q: x2 sin 2x dx 2.1

A:

Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: c) Use trigonometric substitution to integrate dx 4-x2

A:

Q: V3x d. Evaluate dx sin(3t) dt

A:

Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

A:

Q: integral of cos x sin^3 2 x dx

A:

Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

A:

Q: (a) Evaluate xe* dx using substitution method. (b) Evaluate | 6xe* dx using integration by part…

A: We will find out the required value.

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

A:

Q: cos(x² + y²) = y² sinx² y² = ln(x² + y²)

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

A:

Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

A:

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

A:

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

A:

Q: in integrating the function f(3x + 5)(cosar using integration by parts, what would be your du?

A: Solution

Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

A:

Q: 2. Use integration by parts to solve for [x³c x³ cosx dx.

A:

Q: dt dx 3. 6x – x² 4. sin xV1 XN Cos xdx 3x 5. 1-2e3*) 6. dx

A: We solve only 4th question.  Let 1-cos(x) =t

Q: Find dy/dx by implicit differentiation: x3– 3x²y + 2xy² = 12 b. cos (x- y) = x а.

A:

Q: In integrating the function f(3x + 5)(cos) dx using integration by parts, what would be your v? v =…

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu. In general, the ILATE rule is used…

Q: Evaluate / e*cos(x)dx using integration by parts-

A:

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

A:

Q: 2. f x cos² x dx

A:

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: 4. Evaluate x sin2x dx Integration by parts

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: (B): Find the integration by using substitution method √x√2x-1 dx

A:

Q: B4. Evaluate e* sin x dx by using integration by parts method.

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: | (In x)² dx_use integrationI

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = 10x+ 9x2-sin6x

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.