Evaluate the integrals below:. cos3x .dx, b) elsin3x) – 1). a) 0.

Q: b) Express the area of the pool, A in terms of I and r. c) Hence, or otherwise show that A = -² +…

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Q: Evaluate each integral. •23 a) -2 36 dx V16–x² .2 b) | dx 3 4+x

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Q: 2. Use trigonometric substitution to find each of the following integrals. Don't forget to go back…

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Q: a.) √ 1 csc² x+sec² x cosx-cos³x - dx

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Q: d) Let y= Acos2t where A is a constant. Find the value of A such that d y --3y = 9cos2t for all…

A: Given  The equation is  y= A cos(2t) , where  A  is constant  and condition is  d2ydt2-3y=9cos(2t) .

Q: Evaluate the definite integrals -3 a) dx b) 1. 2 c) dx d) x² dx da

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Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: 5. The value of the definite integral 2 dx is A In8 b) In 2 c) In6 d) 0

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Q: 714 a) J116z SE-3") da

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Q: 2 (x+95y)e !!

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Q: Evaluate the integral. .5 11) 6x5 dx -1 A) 624 B) 93,744 C) 15,624 D) -15,624 must show work…

A: Given ∫-156x5dx The Fundamental theorem of integral calculus  ∫abfxdx=Fb-Fa,  If F'x=fx

Q: iR w= f cu) and メコ show that x Jw

A: We’ll answer the only one question since the exact one wasn’t specified. Please submit a new…

Q: Find the distance between 4y + 3x = 4 and point (0, 5) O 3.4 O 3.2 O 2.8 3

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Q: a.) S dx/x²+4x+5 b.) S(cscx – tanx)²dx

A: topic - indefinite integral

Q: Derive a formula for fx* In x dxwhere a.) n+ -1 b.) n = -1

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Q: Evaluate the integral: LIVE 1 I√9r²+25 dr.

A: We will solve the given question using simple Integration rules.

Q: [(3+ csc² x) dx = , r 3x- cotx+C a) 3x-3 cot x+C c) 3x+ cot x+C d) 3x+3 ta

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Q: Find the distance between 4y + 3x = 4 and point (0, 5) O 3.2 3 O 3.4 O 2.8

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Q: Ci-2)x OS how that dx = where cis constant of integratron abore or Otherwise Using find f ansurer -2…

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Q: = 10. The triple integral dxdydz:

A: Here we have to evaluate the given triple integral.

Q: In a class of 100 computer science students, 60 know Python, 36 know Java, and 52 know C++. 18 know…

A: To find number of students that know all of three languages.

Q: Evaluate the integral 12 cosh 2r dr.

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Q: H.co/ prove That;. dz 1-2 Cosh2=

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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.