Let R = M2(Z12). Then A= '5 | is a unit

Q: 1 S. cot ³ x dx

A: I have stated the used formulas in the solution

Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: Evaluate the integral. сп/4 8 sec?(t) dt

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Q: dy Given y = In(tan 0), find 0 such that 4, where 0< 0 <T 2

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Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

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Q: Evaluate L e* dx dy by using trapezoidal and Simpson's rules.

A: Given that, ∫02∫01ex+ydxdy By trapezoidal rule, ∫abf(x)dx≈h2f(a)+2fa+b2+f(b) where h=b-an…

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: make the given substitutions to evaluate the indefiniteintegrals. ∫4x3/(x4 + 1)2 dx, u = x4 + 1

A: Now put

Q: Use the substitution formula to evaluate the integral. T/8 19) (1 + etan 2x) sec 2x dx

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Q: Find the definite antiderivative dx/x^2(sqrt(x^2+36)) from 1/2 to 1

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Q: Evaluate e* dx dy by using trapezoidal and Simpson's rules.

A: Hello. Since your question has multiple parts, we will solve the first integral by first method for…

Q: O Evalmate the impaper mitegral on e Show that it DE VERGES dx x In? (x) 2. tan (x) dx

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Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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Q: Find cosh a In(sinh r)dr.

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Q: Let z=e"In(xy), determine dx

A: Solving the problem by doing partial differentiation.

Q: Evaluate the following integral: (tan(t) sec(t) i – te³'j) dt

A: The objective of the question is evaluate the indefinite integral.

Q: How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

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Q: du Q. Show that du and dy for u = In Vx2 + y? %3D dy and v = tan

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Q: Find the indicated Trapezoid Rule approximation to the following integral.

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Q: Evaluate f w?sin(10w)dw using integration by parts W

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Q: Q1. Let yr 6r 5 be given. (a) Find x and y intecepts (if any of the siven function. (b) Find the…

A: Given that y=x2-6x+5 and we have to find the following: (a) x and y intercepts of the given function…

Q: Using a suitable substitution, the integral T/4 9 (13+tan t)8 sec? t dt of

A: Given,          ∫0π4913+tant8sec2tdt

Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: e) Apply the Fundamental Theorem of Calculus in order to evaluate the definite integral: + 2)* dz =

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Q: Evaluate the integral. 'Tt/2 7 cot (x) dx T/4

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Q: ) 1 1 dx x – 1

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Q: Determine how large the number a has to be so that     ∫a∞ 1/(x2+ 1) dx &lt; 0.001

A: It is given that, ∫a∞1x2+1dx&lt;0.001. Show the definition of an improper integral of type 1: (a) If…

Q: Find cosh r In(sinh a)dr.

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Q: Evaluate the following integral : S (sec X + cot X)² dx

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Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: Evaluate the following integral: (tan(t) sec(t) i – teštj) dt

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Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: DIfterenti are (뉴) de Ipx tan x -In DIfterentiate exy te Yy 1, tnd y"

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

Q: The integral dx is Select one: O None. o o o

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Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: Suppose we wish to evaluate by using integration by parts, where a, bER. Given that we choose what…

A: Let  u=x ; v = e2xAfter differentiating v with respect to x is:dvdx=2e2xdv=2e2xdxAfter…

Q: The integral dx can be evaluated using either a u-substitution or a trig substitution. 4 - True O…

A: Yes the above integral can evaluate using u-substitution and trig-substitution.

Q: Evaluate the following intepal 2y° +y ) y" +y 8+e dy e 2. +1

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Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

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Q: et dx using the substitution u = Evaluate the integral 17 + e*. 17+ ex

A: To evaluate the integral: ∫ex17+exdx. Solution: Le substitute u=17+ex. Differentiating both sides,…

Q: The function f(z) = sinh(In(z ?)) is equivalet to

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Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: dx dy. Evaluate by changing the order 4y

A: In the given question we have to evaluate the integration                ∫01∫4yyex2dxdy by the…

Q: Determine the following convolutions by integration (a) 1 * sin wt (b) et * e

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Q: If y = tanu, u =v--, and v= In x, dy at x= e? what is the value of dx

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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.