3. Find the integral of these Trigonometric functions

Q: Find the trigonometric integral.

A: Integral of a function is the anti derivative of the function, meaning area of the graph of the…

Q: The goal of this problem is to evaluate the indefinite integral /x² 9dx. (a) Use an appropriate…

A:

Q: Evaluate the integral. ∫Sin3 θ Cos 4θ  dθ

A: We have given;

Q: sin 20 arctan(sin 0) d0

A:

Q: What is the indefininte intregal of Tan^-1(3x) / 1+9x^2 .

A: The given indefinite integral is

Q: Evaluate the indefinite integral ∫ sin8 θ cos θ dθ

A: Let and differentiate it with respect to and find .

Q: What is the integral of 1/3(sin^2,theta)?

A: To find the integration [1/(3sin²x)]dx I am writing theta=x just for ease of typing

Q: 3. (sin0 + cos€)²d0

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Calculate the indefinite integral:  ∫ sin(θ − 8) dθ

A: Given: ∫sinθ-8dθ

Q: 1. Find the first derivative of the given trigonometric function 1 z = 4cos?. 2

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Q: Find or evaluate the integral

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Q: Find the indefinite integral.

A: For the given expression:                       We can solve it using substitution method: Now,…

Q: Evaluate the integral. sin COs 503 502 502 sin 50 1. cos d0 3D 502 502

A:

Q: Evaluate the integral of sin^7 (theta) cos^3 (theta) d(theta)

A: Solve integral by substitution method

Q: Evaluate the integral. ∫0 π/2 Sin7 θ Cos 5θ  dθ

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Q: Perform

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Q: Evaluate the integral.

A:

Q: Use a table of integrals with forms involving the trigonometric functions to find the indefinite…

A: Given Data The indefinite integral is ∫11+cot4xdx.   Let, 4x=vddx4x=dvdxdx=dv4   Put the values in…

Q: Find the area between the inner and outer ovals of r = 4(1+sine

A: I am going to solve the given problem by using some simple calculus to get the require

Q: sin xv1 – cos xdx

A: Explanation of the answer is as follows

Q: Derive the integral using one of the methods that we discussed this semester. x cOs xdx

A: We have to derive the integral                                                 ∫xcosxdx

Q: Find the trigonometric integral ∫ tan2 x /sec3 x   dx

A: We have to integrate ∫tan2xsec3xdx We will put tanx=sinxcosx and secx=1cosx Given integral can be…

Q: 8. Find the area enclosed by 1 leaf of r=sin30

A: Let's find.

Q: sin ede 1- cos e 8.

A: The integral of sinθ is given by -cosθ and the integral of cosθ is given by sinθ. The basic formula…

Q: Evaluate the integral.

A: We have to evaluate ∫3sinθ cosθ dθ Let substitute t=sinθ ⇒dtdθ=cosθ⇒dt=cosθ dθ Substituting the…

Q: sec $ x dx

A:

Q: By using the relationship between the hyperbolic sine function and its inverse, prove * (sinh (z)] =…

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Q: Find the indefinite integral: (sin æ) (cosa) dr

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Q: Evaluate the integral ∫1/θ2 sin 1/θ cos 1/θ dθ

A: Given- ∫1θ2sin1θcos1θ dθ To find- The value of the integral. Concept Used-  The above integral can…

Q: Find the indefinite integral f sec*(3x) dx using techniques for trigonometric integrals.

A: ∫sec43x dx On simplification, we get ∫sec43x dx=∫sec23x sec23x dx=∫sec23x 1+tan23x dx…

Q: Evaluate the following trigonometric integral: sin2x cosx dx X, X.

A:

Q: Evaluate the definite integral: 2, 1 sin 0 + cos 0 +1

A: Given that: ∫0π21sinθ+cosθ+1dθ

Q: | cos (5x) cos (3x)dx

A: Given integral: ∫cos5xcos3xdx We know, cosαcosβ=12cosα+β+cosα-β. Also, ∫cosxdx=sinx+c.

Q: What would be the trigonometric identity to be used in order to transform the integral f tan z dz…

A: Topic = Integration Correct answer tan x =sin xcos x

Q: Evaluate the integral ∫cos√θ/ √θ sin2 √θ dθ

A: We have to evaluate the integral: ∫cosθθ sin 2θdθ We know the trigonometric identity, sin 2A=2sin A…

Q: * To evaluate the integral | sin ecos°ede by trigonometric transformation, we use the identity,

A: ∫sin3θ cos6θ dθ

Q: 1) Prove that cos°(x) + sin (x) = 1. (refer to notes). Use the "Square" formula.

A: See the attachment

Q: sin100

A:

Q: (4) |sin² 0 cos0 d0

A:

Q: 16. Evaluate the definite integral cos?

A: Solved below...

Q: Evaluate the integral. 1/2 sin1"(0) cos (0) də

A:

Q: The trigonometric substitution x = = 3 sin 0 has led to the integral I = f tan³ 0 sec 0 de which can…

A: Topic:- application of integration and trigonometry ratios

Q: Evaluate the indefinite integral sin v cos vdv

A: Given: Let I=∫sin3 v cos8 v dv To Find: To evaluate the given integral.

Q: Evaluate the definite integral.

A: The given integral is ∫0π3tan2xdx.

Q: | sin(ax) cos(ax) dx

A:

Q: Find the area between the two curves for a = 13. %3D ,ra+ sin20 P= sin20 (Use symbolic notation and…

A:

Q: The trigonometric integral [sec² x (tan³x - 2 tan² x) dx is equal to

A: SOLUTION-

Q: Evaluate the indefinite integral sin v cOs vdv

A: Given:       ∫3sin4v cosv dv Taking constant out.         =3∫sin4v cosv dv substitute u=sin…