After choosing the appropriate trigonometric substitution the integral 4 x² dx, becomes 4 cos (0)de cos (0)d0 | tan (0)de None 4 sin² (0)d0

Q: Q: 1. Find the value of the following integral: sin vi dx using Simpson's rule when n = 8.

A:

Q: The approximation of the integral f,(x-2) cos(x + 1) dx using two points Gaussian quadrature formula…

A: According to Gauss Quadrature rule, the integral of a function f(x) over the interval [a,b] is given…

Q: Given the integral sec (x - 1) tanª (x - 1)dx, which of the following equations will be useful for…

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Q: 4. Evaluate the trigonometric integral. sin³ 0 cos? 0 de 3

A: Given that,

Q: Using appropriate trigonometric substitution and changing the limit of integration, the integral…

A:

Q: Evaluate (sin z + cos x) da using by term by term integration 0. Answer:

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Q: In the following integral x – 2 dx x² +25 what trigonometric function will be the best to substitute…

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Q: Q2: find the integral of trigonometric function cos sint dx

A: To evaluate the integral: I=∫0πcos5x sin4x dx⇒I=∫0πcos4x sin4x  cos x dx⇒I=∫0πcos2x2 sin4x  cos x…

Q: Simplify the integral 1 dx using an appropriate trigonometric substitution. Va2 +4 Cos e do de sec 0…

A: Hence option (e) is correct.

Q: The integral S³ S S Sse x dx x²+√√x²-1-1 sece tane de sece - 1 cose d 1 - sino sine de 1 + cose…

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Q: Using the trigonometric substitution x = 6 cos 0, 0 < 0 < π, the integral √36-x² x² In cos 0 + C O…

A:

Q: The approximation of the integral f(x-1) cos(x-1) dx using two points Gaussian quadrature formula…

A: Given integral is ∫−11x−12cosx−1dx. We have to approximate the given integral by using two point…

Q: The first step to solve the integral of (sin x)^4*(cos x)^3 dx is transform the problem by using…

A:

Q: The integral A / B © S D x² + x dx can be transformed to which of the following using trigonometric…

A: Explained below

Q: has the form - F(0)+ + C: What should be the value of e to make F(o)=0? The resulting integral of…

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Q: After integration by parts we have e70 cos(80) d0 e70 sin(80) d0.

A: Explained below

Q: Evaluate the following definite integral. 1/6 -2 cos x dx 1/6 -2 cos x dx = -1 (Type an exact…

A: The given definite integral is: I=∫0π6 -2 cos x dx

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. dx…

A: We have to find the integral

Q: 1+I dx Which one is the best substitution for evaluating the integral f cos Oz = u? Or = cos 20 I =…

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Q: The integral sin(x- 2) dx is transformed into f, g(t)dt by applying an appropriate change of…

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Q: ·S- The integral x dx x²+√√√x²-1-1 can be transformed to which of the following using trigonometric…

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Q: The resulting integral of F(@) + + C. What should be the value of e to make F(e= sin -cos-sine de…

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Q: Using substitution with u= sin(2x), the definite integral | 4 sin³(2x)cos(2x)dx is equivalent to (A…

A: The given integral is ∫0π4sin32xcos2xdx.

Q: If the substitution in the integration by trigonometric substitution is z = 3 tan 0, what would be…

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Q: Given: S√-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms of ? 9…

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Q: Consider the integral / sin*+1x - cos x dx , where k is a positive integer. Using the methods…

A: By using u substitution method

Q: (a) Use an appropriate substitution to integrate the following. V1+4x (b) Use a trigonometric…

A:

Q: Evaluate the definite integral 2 (sin t, cos t) dt. COS 7/2 Select the correct anSwer helow:

A: We have to find out

Q: Which of the following is one of the correct steps to evaluate | cos'x dx to obtain the desired…

A: Solution :∫cos7xdx∫cos6xcosxdx∫cos2x3cosxdx∫1-sin2x3cosxdx

Q: The integral B D x dx can be transformed to which of the following using trigonometric substitution?…

A:

Q: The integral cos(x − 3) dx is transformed into f, g(t)dt by applying an appropriate change of…

A: Solution :-

Q: S The integral S x dx x²+√√x²-1-1 sece tane de sece - 1 sec²0 do 1+tano cose dᎾ 1 - sino sine de 1 +…

A:

Q: After choosing the appropriate trigonometric substitution the integral -dx, becomes J4 x O None sin…

A: Topic- integration by substituting

Q: e² sin® (e²) cos' (e²)dx

A: According to question,Given Integral,Let I = ∫ ex sin6ex cos7ex dx

Q: Consider the integral cos“ x · sin'x dx , where k is a positive cos“ x• integer. Using the methods…

A: ∫coskx . sin3x dx∫coskx . sin2x .  sinx dx∫coskx . (1-cos2x) .  sinx dx               ( sin2x =…

Q: 9. Find the area of the region in the first quadrant that is inside r = 4 sin 0 and outside r2 = 8…

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Q: 12. By using the trigonometric substitution X = x = ; + sin(0) then the integral S - xp- (3+4x-4x2)…

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Q: The integral O x dx can be transformed to which of the following using trigonometric substitution?…

A:

Q: e resulting integral of s sin sin(0) do has the form --F(0)+ mat should be the value of 0 to make…

A:

Q: Using substitution with u = sin(2x), the definite integral sin (2x) cos(2x) dx is equivalent to ...…

A: Use substitution

Q: s After an appropriate trigonometric substitution, the integral transformed into which one of the…

A: Concept: The trigonometric change: The trigonometric identities can be used to assess several…

Q: Is it possible to use the reduction formula for cosine on this integral?  ∫[(1 - cos^(2)Θ) * cosΘ]…

A: Given,

Q: x = 9 tan 0 is an appropriate trigonometric substitution for the integral Select one: O True O False…

A:

Q: The resulting integral of sin-cos- sin@ do has the form -F(0) +C• What should be the value of o to…

A: Integration

Q: The approximation of the integral (x-2) cos(x+ 1) dx using two points Gaussian quadrature formula…

A: To approximate the below integral using two points Gaussian quadrature formula. ∫−11x−22cosx+1dx

Q: To evaluate the integral x² dx, x² -4x + 20 using trigonometric substitution, which substitution…

A: Answer is option B.

Q: Using a suitable trigonometric substitution, the integral dx 3 (16x² + 9)² is equal to sin 8+ C₁-<<…

A:

Q: (10,00 Puanlar) /6 7 - What is the value of the integral sin(6x) arctan(sin 3x)dx? c) “ d) 6(1 - 2)…

A: This question is related to integration.

Q: If you are going to evaluate the integral f cos x v9 + 25sin-x dx using trigonometric substitution,…

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Q: 1.Evaluate ∫[tan^3(θ)/cos^4(θ)]dθ  2.Evaluate ∫cos(x)e^(sin(x)) dx 3.This result is a…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.