2 sin(t) s(t) = et

Q: J cos x sin x V1 + sin² x dx

A:

Q: 7 sin°(e) cos"(t) dt

A: To evaluate the given definite integral

Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

A:

Q: -을 x e [T, 3 J Sinx =

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Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

A:

Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: nasin(hx) cos(bx)dx

A:

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

A:

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: 2 cos x dx, 1+ sin x (c) t = sin r. 0.

A:

Q: S+ xcos (nx) dx + (π-x)(cos(nx)) dx

A: Here we will use integration by parts  let f(x) and g(x) are two function of x then…

Q: |3 cos(2x – t/ 2) cos(x+ t/ 4)dx

A: To evaluate the integral: ∫3cos2x-π2cosx+π4dx Solution: We know that, cosa cosb=12cosa+b+cosa-b…

Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: | t sin(2t) dt 1.

A:

Q: y = sin x, y = cos.x , x= 0 , x=- is revolved about the x-axis T/2

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Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

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Q: fo (9 cos(x) – 2 sec²(x)) dx

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Q: 5. x- + Px = sin t %3D dt

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Q: ( sin(3x) e **) + 32- – 4y = 4x (By u x2 (-1-4) (4)(3:5) dx

A: As per the bartleby guidelines for more than one question only one has to be solved. Please upload…

Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

A:

Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

A:

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: 8. y = In(2e-t sin t)

A:

Q: S cos(3x – 2n) cos (x + t) dx

A: We know that, 2cosAcosB=cos(A+B)+cos(A-B) Also, ∫cosxdx=sinx

Q: b) S. cos x cos 7x dx

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Q: cos x II. S .dx V1-2 sin x III. Stan³x sec*x.dx

A:

Q: I) sin X dy dx Sin 2X - y Cos X

A: Explanation of the answer is as follows

Q: dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

A: According to the given information, it is required to find the general solution.

Q: cos 3x b. S; dx = ... 3+15 sin 3x

A: We have to solve the given integral .

Q: .2. COS X sın.x.ços.Xdx

A:

Q: トキ 4 Sin Yx cos? dn SinYy

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Q: x cos x² 2. X C0 dx -siny

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Q: g. cOS x Vsin x dx

A: Let sinx = t

Q: 3x e COs x dx

A: To evaluate:∫e3xcosxdx

Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

A:

Q: 11. sin(x) + cos(y) = ey

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: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

A:

Q: I sin(z) cos I) COS(2C (x) dx %3D

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Q: dx I [; (1-2x) I= [sin (4x) cos(4x)dx (In(x))3 dx I

A: Given

Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: d rIn(x) t tan(t) dt|. dx -1

A: we have to evaluate the following

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

A: solution.

Q: x2 sin3(x) Q.2\ Find dx if y = In cos(x*).V1+x/

A:

Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

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

Q: d le" cos.x) cOS x dx

A: Given ,  d/dx(ex cosx)  We know that  d/dx(uv) = u'v + uv'  Here ,  u = ex and v = cosx Then ,

Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.