7) (1+x')dy + 2xydx = 0

Q: S(x*+1)(x* + 5x)'dx 11.

A:

Q: 5. fx³ cosh¯¹(x²) dx

A:

Q: 2 cosh x +losion2x = 5

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

Q: [xVtan x² sec* x² dx -

A: Given,         ∫xtanx2sec4x2dx

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: dy 5. x- 3y = x². dx

A: (5)We need to find the solution of given differential equations

Q: If y=+*+9x²+26x+24 gấp 46 find f'(2).

A:

Q: 13.9y" +12y + 4y = 0, y(0) = 2, y'(0) = -1

A:

Q: 5. Find y' for y=³√ 3√² + 3√/2

A: The given function is: y=3x2+53x As we know that, The Sum/Difference rule: f±g'=f'±g' The Power law:…

Q: 5. If y=5x²-3x + 10, give y'(-1)

A: We have to find the y'(-1).

Q: 1. S dx x³+2x x2+1

A:

Q: 20) S(tanh (4– 3x) kdx

A:

Q: (2x+3)5

A:

Q: 5. (1-x) (dy/dx) + xy = xy". Ans. cy=(1-y)√(1-x)

A: Given equation is 1-x2dydx+xy=xy2. To find: solution of the given equation.

Q: /x²-1 dx

A: We use substitution and basic trigonometry properties to solve this. Integration may have different…

Q: 11. x² +1 Find +3x+1 -dx

A:

Q: S(2x3 + x)V2x² + 1 dx

A:

Q: (+っ)dx - 2xydy=0

A: Differential equation.

Q: 4. x(x² – 1)² dx

A: Solution:

Q: '5 '5 '5 If f(x) dx = 33 and g(x) dx = 14, find [2f(x) + 3g(x)] dx. %3D

A:

Q: S t /1+3t - dt

A:

Q: Suppose dy/dx= (3x+1) √(3x^2+2x) and y(0)=1. what is y(5)?

A:

Q: Integrate √ 2²4 x²ln(x) dx.

A:

Q: 10. f(3x - 1)(x - 1) dx

A: The given integral is:∫-113x-1x-1dx

Q: 29.

A:

Q: 9. dx J1 (3x²+1)3

A:

Q: 6. (D² + 1)y = 10e* sin x

A: see below the answer and explanation

Q: 4. S Vx(x² + 2) dx

A:

Q: 2. y' (4x - y₁)² = 0 -

A: This is an ODE problem.

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.