5) [ Arc sin- xdx

Q: 3.) y'of y = arccos[arcsin ()

A:

Q: tan x[cot x – cos x]dx

A: Here we can find the integration as below

Q: 28. tan (2x) sec (2x) dx

A: follow the procedure given below.

Q: 5. Integrate: [tan(7x)dx

A: 5) The given integral is ∫tan7xdx

Q: Evaluate S(cos4 x – sin* x)dx

A:

Q: In [tan (5 + )| +o sec x dx 4 2

A:

Q: 2. S tane sec4 0 d0

A:

Q: 1+3x – cosI 2.) lim tan x

A: limx->01+3x-cosxtanx When we plug in 0 for x then we get…

Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ      ∵cos2x=1-2sin2x=2θ=2…

Q: 3. (6れ)-) ANCTAN X (x+1) ² -y=ARCTAN

A: To expand the given function :

Q: Show that Cosx dx 9- Sin 3D

A:

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: |12 sin(4x) cot(cos(4x)) dx

A:

Q: If tanh(x)=5/13, what is the sinh(x)?

A: Answer is sinhx=5/12. Explanation is given below..

Q: 11-­ Use linear approximation to estimate sin29(degree).

A: Given, sin 29° To find: Value of sin 29°using linear approximation

Q: Expand fix)= Sin(x+ TT),O<X< I ina half range sine series

A:

Q: 7. Integrate. S tan50 sec³0d0

A:

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

A:

Q: Show that cos( arctan( sin( arccot(x)))) = sqrt{{x^2+1}/{x^2+2}}

A:

Q: 5. | sin (Tx) cos (Tx) dx

A:

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

A:

Q: Evaluate S (cos4 x – sin“ x) dx

A:

Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

A:

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

Q: 4) The curver= V1 + sin20,

A: Solution :-

Q: 7. Evaluate Arc cos(j2).

A: It is principal value.

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: .15 S sin²4y cos>4ydy

A:

Q: 12 tan (4.x) sec (4x) dx S cos(11x) sin(2r) dx COS

A: Given that integration and we solve this integration by using general formulas of integration. Here…

Q: (7) Find sin(5x) cos(4x) dx

A: Topic:- application of integration     Note:- as per our guideline if more than one question…

Q: 7. Show that sin (+ x) = -cosx.

A:

Q: Determine the length of the arc y=ln(cos x) for 0≤x≤π3.

A:

Q: 13T (b) sin-(sin(- -)) = %3D 11

A:

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: 9, 9. tan 2x dx 0.

A: Integration basically means to find the integrals, i.e., to assign numbers to function in such a way…

Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: 15. Evaluate | sin° x cos xdx 3

A:

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: E prove that - Cotx + C 2 |- Cosx +Sinx

A: Solve the integration

Q: Evaluate 1) S sin ³x cos³x dx

A: Given: ∫sin3(x)cos3(x) dx

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

A:

Q: 2 Arc cos (1- y=

A: Given,   y=2arccos1-x2+4x-x2.   It is differentiated as follows:…

Q: . Evaluate S sin' 2x cos 2x dx

A:

Q: Compute sin x et + 3e-x

A:

Q: Find ∫sin 5x cos 4x dx.

A: Given, ∫sin5x.cos4xdx

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.