SIixdx 4. cosxa/5+ Ln°cosx 2

Q: dx 1+cosx 2.

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Q: IX. Find y' if 1. (5 pts.) y = 2 In (cos (Tx)) 2. (6 pts.) y = csc² (Arcsec (Va) + e-)

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Q: a.) Evaleiate. (6tanx dx

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Q: S cos(2x)e2* dx (recurring)

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Q: cos y = e

A: Need to find differentiation for given function

Q: S cos32x dx.

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Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: 1 36* dx V6* + 3

A: We have to find

Q: x10 14) cos Vt dt )음 COS

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Q: 1 e xvx-1 dy dx 1 a),{ In |0* + 1|} ,b) arctan (V02 – 1) c) sec-1(0²) – 1 |

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Q: cos(15x) cos(4r) dx

A: Given∫cos(15x)cos(4x)dx  ...(1)For the simplification apply the trigonometric identitycos(a…

Q: 7. S (x-1+cosx) cos2(sinx+lnx)

A: We use substitution method to solve this integration

Q: 2TT Sin nx dx

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Q: Evaluate fe.cos 2x dx

A: ∫e3x cos2x dx

Q: cos8x 8.S -dx sin4x os³tdt dt 9. Ste 1-sint

A: Given the integral

Q: х cos(5x) dx —

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Q: dy Find dx if y = cos e*

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Q: Find integral.

A: Consider the indefinite integral ∫-6x cos 5x dx Use the integration by parts to solve the indefinite…

Q: , Sercoszx *cos2x dx 3.

A: Since multiple questions are asked answering the first question, repost other question for solutions

Q: ю 2ах—х e la dx Use gamma or beta laws

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Q: 22. (-5) dx dy

A: Given: ∫-4-1 ∫48 (-5) dx dy To find: Value of the integral.

Q: Cos^3(3x) dx

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Q: S cos 2x dx COSX

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Q: - Si * dx dy

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Q: Question:4 Calculate dx by implicit derivatives (tan x) + ycotx + sinxy – exy – In2 = 0

A: Differentiate the equation implicitly:

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: 2ах — х e la dx Use gamma or beta laws

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Q: L{cos 5t} OS

A: To find the laplace transform of cos2 5t. We use the cosine formulas to solve the given question. We…

Q: S cos(7x) cos (18x)dx

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Q: Calculate L{e-# cos(2t – r)}

A: We have to calculate : Le-2tcos(2t-π) First we will calculate , Lcos(2t-π)…

Q: S Arctan2x dx

A: This is to be solved by the technique called integration by parts

Q: cos (4x)dx

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Q: Grade: 107.5/156 Print Version dy sin(5æ) Find for y dx dy Preview ||

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Q: 3x Cos 2x dx

A: Simple use integration by parts method.

Q: cos(3x) dx

A: answer is in next step

Q: 8. Sedr cos 2x dx

A: Integration of e3x cos2x

Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: 16 ) d du -1 cos и — 1<и<1 dx V1 – u² dx

A: As we know that the differentiation properties:- chain rule: ddx(f(g(x)))=f'(g(x))g'(x)…

Q: ∫cos^4 2x dx

A: Please see the answer in step 2

Q: 10. cos (1/) dx

A: We have to evaluate the indefinte integral as shown below:

Q: 6. Find dy/dx and simplify y sin = - х

A: According to our policies we are allowed to solve one question at a time so kindly repost other…

Q: S cos 8x dx

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Q: 211 211 ( cos nx dx= | [cos nx cos nx dx 0.

A: given that                               ∫02πcos2nxdx=∫02πcosnx cosnx dx=0 now,…

Q: S cos(2²) dydz

A: The integration given is ∫0π∫yπcosx2 dydx. The limit in the given integration is,0≤y≤π , y≤x≤π The…

Q: 1. ſ e*sinx dx

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Q: Se-3x cos(5x) dx

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Q: Ns dy dx

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Q: d) cos (5æ) cos(7r)dx e) S tan e sec“ rdr

A: we have to find the following integral

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.