Evaluate f(x) = 7sin r 1 COS -X %3D at a /3. x =

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: Find y' for y = ecos x + tan-1(5x) + (5x² + 1) ?

A:

Q: 4. Integrate: 5dx dx a) f b) [ c) f- 1 dx; d) x' V16-x? 1+ cosx cos x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: Find for the following function. dx 6 cos x y = 6-5 cos x dx

A: To find the derivative of y.

Q: Evaluate ]e * cos (7x) dx. Seex cos (7x) dx = %3D

A: Explanation of the answer is as follows

Q: 2FI 2FI sım nx dx = cos nx dx = 0, where n integer. 0.-

A:

Q: e) y = In(cos 4 x) f) y = sin² x y = In(cos(e3*)) g)

A: We can solve using first order differentiation (using chain rule)

Q: Find the slope of the curve 2xy = In(e2*) sin(x) at the point (2,2)

A:

Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: y' – 3y + 2y = cos(e-")

A:

Q: Find d²y/dx². y=xsin x 10 cos x

A:

Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

A: I am attaching image so that you understand each and every step.

Q: Ssint2x)dx = 2cos(2x) (2x) + С -cos(2x) + C O 2 cos(2x) -cos(2x)+ C

A:

Q: tanr sec r dx 3

A: Here we will find the antidarive.

Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

A:

Q: 11.) F sin (x)cos²(x)dx 2

A: Note:   As per our company policy we should answer only one question each time, so please repost the…

Q: "/2 sin x dx Jn/a V1-2 cos x 4.

A: As per the guidelines  we can answer only one question at a time. If you want to get the answers  of…

Q: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: 2. If y = e-* cos 2x, then f'(x) = %3D

A: Given : fx = e-xcos2x

Q: Find the antiderivative of f(x)=cos(3x)

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: 3x d. Evaluate dx COS cos (3t – 1) dt

A:

Q: d (i) Show that (2 dx -1 X 3x x tan 3 = tan-1* 3 x2+9 V3 i) Hence evaluate (tan dx . 3

A:

Q: Find by implicit differentiation: dx a. cos y =x+ y

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: .2. COS X sın.x.ços.Xdx

A:

Q: cos xdx (vii) S 5+sin2 x

A:

Q: ution of y" + 4y = cos 2x b

A:

Q: The antiderivative of Cos(3x)

A:

Q: Find dy/dx of the function below. 2x³ + e^(2y) = cos3y

A: 2x3+e2y=cos(3y)Differentiate with respect to…

Q: Find d²y/dx² implicitly in terms of x and y. 4xy 5 cos(x) = -9 d²y dx² || X

A:

Q: cos (x) J = g(x): x2

A:

Q: find dy/dx. g(x) = cos x/sin2 x

A:

Q: Find y' where y = cos (ze19 =) – gec = Cos ( xe-

A: on doing differentiation with respect to x we get option C

Q: find dy/dx. ƒ(x) = x3 sin x cos x

A:

Q: (c) Find dy/dx by implicit differentiation cos(x² y) = x

A: We are given, cos(x2y) = x We need to find dy/dx

Q: y" – 3y' + 2y = cos(e-*)

A:

Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: e) cos (x + y) - cos(x - y) =-2sinxsiny

A: The LHS of the given equation is cosx+y-cosx-y. Note that, cosA+B=cosAcosB-sinAsinB and…

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

A:

Q: Integrate using substitution: [x* cos(x' )dx

A:

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

A:

Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

A:

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

A:

Q: (b) Determine J cos(x²) 2x dx by using substitution method.

A:

Q: Q1) Show that: (a) (1+x)° =1+6x :(cosx) = dx = -sinx (e)읊 = E d ( V) = (d) V1+ tan x = 1+;x dx 2 vx

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: E valuate dx 7-3 Sin X +6 Cos X

A: solution.

Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

A: We need to find dy/dx.

Q: Evaluate the dy/dx> d) y=e-x((cos(2x)) a) -e-x(cos2x+2sin2x) b) e-x(sin2x-cos2x) c)…

A: y=e-xcos(2x)differentiate…