2-) Calcu late +he folloming integ rols by using the integration met hods a)| (hx" +8x²+ 15x) dx dx Vx?+ hx Sinx,cos?y

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: Integrate {w^7 * cos(3w^4)dw

A:

Q: Integrate: S sin3x cos²x dx

A: The given integral is ∫sin3xcos2xdx

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

A:

Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

A:

Q: 2 [(3 sec2 x + - x)dx 4

A: Integrate

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

A:

Q: 4sinx+sinxsecx dx cos²xV4+secx

A:

Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

A:

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: Evaluate the in tegrol : S sin 5x cog3 5xdx

A:

Q: Ssec? [sec(4x)tan(4x) dx (p sec (5x +3) dx e) f sin 3x + 1. dx 2x +4 f)

A: We will solve the following

Q: d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above…

A: Here is the, solution

Q: 9) S 2 cot 2x cos x dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 11 .7. Determine: / 3 (2 – 5x')"(7xº – 15a²)dr J 3x+5

A: We will evaluate the given integral.

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.