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

Q: 1 2. Evaluate =dx using the trigonometric substitution x= 2 tan0. 2 Vx + 4

A: As per honor code, we will answer the first question for you. Please submit the other as a separate…

Q: cos(x)In(1 + x²) + æ4.8 dx. Evaluate 1+ el.69z – 42.8 answer =

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Q: 10. sin-'x dx 12. p° In p dp 14. s2' ds

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Q: ANSWER iv dx ANSWER S sin(ax) cos(ax) dx

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Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: • Tt X 2. sin? cos cOS dx 2 2

A: To solve this I have used the Beta Gamma Integrals. Some of the Results which I have used is given…

Q: Evaluating √√9-x² dx using trigonometric substitution will lead to: 57/2 A 18 "/2 cos²0d0 35*1/2 B…

A: ANS: B

Q: Evaluate dx 1²√√²-49) SV x>7, using a trigonometric substitution.

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Q: The x2- 4 dx can only be evaluated using trigonometric substitution technique . A True B) False

A: To find if the given integral can be solved only by algebraic substitution technique.

Q: The x² – 4 dx can only be evaluated using trigonometric substitution technique . A) True B False

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Q: 3. -2x sin 3x dx

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

Q: 6t e * sin 4t

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Q: 44. Use the accompanying figure to show that sin-x dx. sin x dx y = sin y = sin x

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Q: Which of the following is equal to J: x2 dx ? A. sin-1 (t) + € B. sin- (t) + € Option 1 O Option 2…

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Q: a) (sinx + cos 2x)dx (+1) do b) S dx c) S (x+2)(x2-6x+5) 8 cot(In 8)

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Q: d Find dx (sin? (In x)]

A: We can solve the given problem using chain rule of derivative. According to the Bartleby guidelines…

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

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Q: 4 Using trigonometric substitutions, S dx is equal to: xV16 – x²

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Q: T/2 S sin? x cos5 x dx

A: Topic = Integration

Q: Substitute the expressions for u and for du to write tan(5x + 8)dx in terms of u. tan(5x + 8)dx = |…

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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: EVALUATE -dx + 144 ,2 O x – 12tan-1 12 none 1 -sin' 12 x – -1 +c 12 O x – tan-1 12

A: We have to evaluate  ∫x2x2 + 144 dx. We know,  ∫1x2+a2dx = 1atan-1xa + C      (where C is constant…

Q: S COSA Sin 2X. C dx

A: We have to find integration

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

A: The given integral is ∫sin52xcos32xdx.

Q: Find the e and simplify whenever possible. dx 1. ут 1-cos 4x sin 4x

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: B) Find and if x sin 3z and y = tan 3z dx

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Q: E sin 0 de

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

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Q: (a) L{t+ sin 4t – e cosh nt} -

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

Q: L{e_t (3 cos 6t 5 sin 6t)}

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Q: 1. Use a substitution to find (6a2 + 2)e*+# dx showing working.

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Q: find dr/dθ r = (1 + sec θ) sin θ

A: We are given: We need to find derivative or r. Distribute sin function we get: Now we can take…

Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: Solve the differenttal equat on 1y +dy_64=12x-50 Sin 2x dx? doe

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Q: S= dx 3+ sinx+cos X

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Q: 0 sin√xcos√x √x dx is equal to

A: To solve the given integral

Q: x³ sin (x²) dx is evaluated using IBP, the value of v du When A 2 sin (x2) -2 sin (x2) none of the…

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Q: Evaluate : L [ ezt -3+sin h t sin

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Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

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: (b) If y = sin (m sinhx), find the value of (yn)o ·

A: Given   it has to find nth derivative at .

Q: 2 tan-(x)dx = %3D O V3 - In (8) TC -In (4) V3 О 2п - In (4) v in - In (4) - 2V3 O None -In (2) V3

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Q: cos x -dx = sin x O A. In 3 В. In e C. In 2 D. In 4 B.

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Q: L, 4x(1– x²)dx S 2 i) ii) -) dx ? (х + Sin?x

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Q: J ? x sin 2x dk

A: This integral can be solved by the method of integration by parts which is given by

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.