If the substitution in the integration by trigonometric substitution is z = 3 tan 0, what would be the answer in the integral of the ending output is sec 0 - 0+ c? O Vz?+3 arctan + c 3 - arctan r +c 3 V49 - arctan +c 2243 arctan r c 3.

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A:

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A: Given that,

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A:

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A:

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Q: S dy 2 2 +1

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A: We know that integration of sinx is - cosx and we know that trigonometry relation is  Sin2x =  2sinx…

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A:

Q: Step 2 To find the integral x Cos Bx dx by the parts fomula, us sin , as Used in the previous step.…

A: Integration by parts ∫u.vdx=u∫vdx-∫dudx×∫vdxdx To find: ∫xcos8xdx

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Q: Without computing the integrals, which of the integrals ſf tan '(x) dr, ſí tan '(VI) dr, and f tan…

A: Let's find.

Q: 2. / 3" csc²(3") sin“(3") da (3") sin®(3") dx

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Q: Consider the integral | cos* x sin'x dx , where k is a positive integer. Using the methods discussed…

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A: Use, sin2(t) + cos2(t) = 1         sin2(t) = 1 - cos2(t)

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A: We will find the value of theta.

Q: valuate the integral. 10 sin?(x) cos3(x) dx CoS

A: Perform integration

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A:

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A: We will evaluate this integral as shown below

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A:

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A: Topic:- application of integration and trigonometry ratios

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A:

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Q: Evaluate the integral. 1/2 |[ cos ti- 3 sin 5t j+ sin? 6t k] dt 1/2 |[cos ti-3 sin 5t j + sin? 6t k]…

A: we use Trigonometry identities to solve this integration

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A: Given :

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A: Answer is  following.

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Q: Evaluate the integral. I sin sin (3x) cos(6x) dx = NOTE: Enter the exact answer. + C

A: We can answer the integration as below.

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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.

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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.