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Q: Find the indefinite integral: cos ( πx ) dx sin, ( π )

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Q: Find the indefinite integral.

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(2x) dx 15 + cos?(x)

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Q: Find the indefinite integral. (Use C for the constant of integration.) 4. do cos(0)

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos' (0) sin(0) dO

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

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Q: ind the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of in 5 dx…

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Q: Find the indefinite integral.

A: The question is taken from the calculus in which we have to find the integral value of given…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(2x) dx 27 + cos (x)

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Q: Evaluate the indefinite integral. (Use C for the constant of integration. | cos(7/x13) dx

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Q: 1 * dx 1+ sin x + cos x

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | Vx19 sin(4 + x21/2) dx…

A: Since the exact one wasn't specified we'll answer the first question only. Please resubmit a new…

Q: Find the indefinite integral. (Use C for the constant of integration.) | (2 cos x + 9 sin x) dx

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Q: Find the indefinite integral. (Use C for the constant of integration.) sin3 50 cos 50 de

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Q: Find the indefinite integral. (Use C for the constant of integration.) sin3 40 cos 40 de

A: Given:   you can solve this question using substitution.

Q: Evaluate the integral.  integral sin 3  x cos 5x dx

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) ∫(sin…

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Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Find the indefinite integral. (Use C for the constant of integration.) sin x 6 + cos2 x xp

A: indefinite integration

Q: 2. Find the following indefinite integral. et cos cos (3x)dx

A: To evaluate ∫excos(3x) dx

Q: Find the indefinite integral. (Use C for the constant of integration.) (4 cos x + 7 sin x) dx

A: Given the integrationI=∫(4cosx+7sinx)dx

Q: Find the indefinite integral. sinh(4 - 7x) dx Step 1 First, let u = 4 - x. Now, differentiate u with…

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Q: Evaluate the integral (1+lnx)5/ x dx from 1 to e.    Find the indefinite integral: sin(x)…

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Q: Use a suitable substitution to find the indefinite integral S csc(sin 0) · cos(0)d0

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Q: Find the indefinite integral

A: To find the indefinite integral: ∫sinx7+cos2x dx Solution: Let substitute t=cosx Differentiating…

Q: Find the indefinite integral. | x cos 9x² dx

A: Given : ∫xcos(9πx2)dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | sin(76) sec (cos(7)) dt

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin20(x) dx

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Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: If we are asked to find the indefinite integral of cos® x sin' x, which identity can we use to…

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Q: Find the indefinite integral. sinh(8 - 9x) dx Step 1 First, let u = 8 - x. Now, differentiate u with…

A: Explanation of the answer is as follows

Q: Find the indefinite integral. (Use C for the constant of integration.) (4 cos x + 5 sin x) dx

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Q: (a) Integrate the following definite integrals by using suitable method: (i) S tan-1 x dx

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Q: Find the indefinite integral ∫ cos2 x sin4 x dx

A: Given: I=∫cos2xsin4xdx we know that ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xn                   ..1

Q: TC 4. sin(2x) cos(2x) dx

A: To evaluate the definite integral

Q: cos (x)sin(x)dx

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Q: Evaluate the indefinite integral: cos° x sin x dx

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Q: Find the indefinite integral using any method ∫ sin   cos   d

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Q: .. a) Show that sinh(2x) sinh(x). = 2 sinh(x) cosh(x), using the exponential definitions for cosh(x)…

A: Hyperbolic functions are defined using exponential functions. The hyperbolic function sinhx is…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x)/sin^20(x)    dx

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Q: Use an appropriate u-substitution to evaluate the indefinite integral 3sin (71)cos(7)dt. Use C'for…

A: Use substitutions to integration

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: Evaluate the indefinite integral. cos x dx (sin x)27

A: Let's find.

Q: Find the indefinite integral ∫ sin x/(1 + cos x)   dx

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Q: Find the indefinite integral. (Use C for the constant of integration. 9. de cos(8) – 1

A: The given integral is ∫9cos(θ)-1 The trigonometric identity is cos θ=1-2sin2θ2 Integration of…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin 1 (x) xp

A: ∫cosxsin16x dx

Q: Find the indefinite integral by using appropriate substitutions. (In(sin.x) dx tanx 1) (n(sin(x)))?…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration sin(2x) dx 31 + cos?(x)

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Q: Evaluate the indefinite integral. 2 sin° (x) cos(x) dx +C

A: In this question, we need to evaluate the given indefinite integral.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(2x) dx 46 + cos?(x)

A:

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.