Using appropriate substitution, ſ sin1º(x)cos³(x)dx is equal to: an

Q: dy If x=5+cos20 and y=3- sin20 , what is ? dx

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

Q: sin x dx cos5x b.

A:

Q: 4. e2x sin e*d x, use algebraic substitution

A: Given :  Intergral ( e2x sinex dx)

Q: tan(e-2x) In(cos(e-2*)) dx 5 S е 2х

A: We have to find out

Q: sin in dx X COS21nx

A: A detailed solution is given below.

Q: Solve the fllowing D.E +4y= cos x - sinx 2. CoS X %3D

A:

Q: Using an appropriate substitution, the integral cosxe+2 sinx) dx is equal to:

A: Solve intregal

Q: L, sin 8x cos 15x dx

A:

Q: S"(e*sin²x – e**cosx) dx B)

A: The formula of integration using by parts:       ∫fg' =fg - ∫f'g

Q: FIND DY/DX OF THE FOLLOWING 3. y-tan (1+sinx)

A:

Q: (cos 12/1- x2 1 1. Evaluate dx by using appropriate substitution. an

A: Evaluate ∫01cos-1x2121-x2dx

Q: Consider the implicit function. e = sin (4x) dy in terms of x. dx Determine the formula for dy dx

A:

Q: a) y = sin x² cos 2x 4.

A: Given: y=sinx2cos2x, y=cos4sec23x We know that ddxuv=vdudx+udvdx…

Q: d e) (In|sin x)) dx

A:

Q: T Cos x-sin x Jr x² dx So

A:

Q: 10. f sin x dx 25+cos²x

A:

Q: (c) Show that e* sin(x²)dx < e – 1.

A:

Q: dv 4+ ecos(sin-w)

A:

Q: Derive y = e*+1 sin x³,

A: To find the derivative of the given function we use product rule of differentiation,  chain rule of…

Q: d (cos x) H.W.: show that -sin x %3D xp

A: Given: To show ddx(cos x)= -sin x Definition : Derivative of f(x) w.r.t. x is defined as:…

Q: Consider b. () 2: x dx e-2 sin 5 a

A:

Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: Use the method of substitution to evaluate | 2x cos x? dx.

A:

Q: In the given question, verify the identity:-   sinh 2x = 2 sinh x cosh x

A: To prove  sinh2x=2sinhxcoshx.

Q: Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

A: Using definition of composite function.

Q: Ly = Ce* + C2 cos x + C3 sinx

A:

Q: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

A:

Q: I= ( cos(In(x)) dx 13- I =

A: GIven that: I=∫cos(ln(x))xdx

Q: When |x3 cos(x?) dx is evaluated using IBP, the value of v du is? cos(x*) - cos(x³) -cos(x*)

A:

Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: (a) Find dy for dx = In (3x – 2) (tan 2x) -

A: Explanation of the solution is given below..

Q: (a) S sin³ cos dx . 3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find ∫cos3 x dx.

A:

Q: . Estimate the root of the expression, f (x) = x² – cos x, using: d. MOSS using xo = -1 with error…

A: As per the question we have to find the root of the equation : f(x) = x2 - cos(x) = 0 With tolerance…

Q: So cos(Anx) dx on lo0) (0,00)

A:

Q: Eliminate the arbitrary constant ln y = c, sin 3x + c2 cos 3x + 9x^2 -2

A:

Q: Find ∫cos4 x dx.

A: To Determine: find the integral ∫cos4xdx Given: we have an integral  Explanation: we have an…

Q: a (a) L{sin at}=- s2 +a?

A:

Q: What is the value of k so that dx sin(kx2) = 6xcos(kx²) ?

A: Topic - derivative of a function

Q: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: To evaluate 1 dx 25+x2 the trigonometric substitution x = 5 sint

A:

Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: Consider the implicit function. e' = sin (6x) Determine the formula for in terms of x. dy dx

A: Here we have to find the derivative.

Q: Using a similar method to above, that is, integrating by parts twice, the following result may be…

A: In this question we have to prove Integration by using Integration by parts.

Q: Integrate the following: 2х-1 a) 3x-2 d) /sin? (3x) cos' (3x)dx | cos* (5x)dx 4. g)

A: (a) Consider the given integral as ∫2x-13x-23dx. Evaluate the above integral as follows:…

Q: If f(x)=e^2x cos(3x), then f’(0) = ?

A: Derivative Question

Q: Solve the definite integral e(arcsin(r)) dx. V1- 22

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.