11 Evaluate || sin(y)dydx where 2: 0

Q: 9 NO ION If g(x) = [ cos t dt, find g '(x). %3D x10 -sin (x) -10x cos (x) COS 1 cos (x°) %3 10x9 cos…

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Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: 2 lim In (cos x)e

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Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: 11) fx-In x dx In x- 2 4 (ans. : -+c) 12) fx- tan'x dx (ans. : 2 -tan"l x -(x- tan"" x)+c) 2 13) fx'…

A: 11.Given,∫x.In x dx

Q: | cos(5x) sin(13x)dx = 1 sin(&x) ) sin(18x 4 6. OB. - 5 sin(5x) sin(13x) + 13 cos(5x) 1 cos(1&x)…

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Q: What is the antiderivative of g(x) = 2 cos(x) that contains the point (7, 0)? 4 O 2 sin(x) –V2 O 2…

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Q: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: Ruestion 13 Evaluate the integral. x4 - 3 dx 2 16 + x o 3.253x + tan 1주 + 253 글x-16x + tan1 +C 16x +…

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Q: 1. Find the critical numbers of f(x) = 2 cos(r) + sin (x) %3D

A: Given: f(x)=2cosx+sin2x  A number is critical if it makes the derivative of the expression equal 0,…

Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

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Q: 1. F (x) = sin x+ 2cos x – 5 %3D 2. G(x) = 3e* – 7log;x – 2 * 3. H (x) = 4sec x + 5tanx 4. Z (x) =…

A: Since there are multiple questions. We will solve only the first three questions. If you want to…

Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: 7. Determine f(x) so that Scon cos(In°x)f(x) dx = sin(ln²x) + C 2 Inx (a) 2 In x (b) In x (c) (d) 2

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Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…

A: Here we use the other formulas with the given one and also use substitution.

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: 13. Evaluate the indefinite integral fx cos x dx x sin 2x cos 2x a. + c 2 x sin 2x cos 4x b. + c 2 2…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

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Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: The limit in lim (46 x; - 28 sin (x;)) Ax i=1 on the interval o, is equal to 2 (23 x² + 28 cos (x))…

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Q: 3. Find the critical numbers of the function f(x) = sin2 3x + cos 3x , 0 <x < 2/3:

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Q: Evaluate the integral cos"() sin(x) dæ cos'4 using the substitution u = 1 = cos(x). | cos"(x) sin(x)…

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Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: I need solution to this problem.

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Q: (1) y = In(x+ 4)- x tan (2) xy + xy x + 3y (3) Iny e' sin

A: In this question we will use basic of calculus i.e concept of differentiation. We will simply…

Q: Differentiate y= sin'x- cos³x CO A. 3sin x cos x (sinx - cos x) COS B 3sio x cos x (sinx + cos x) C.…

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Q: Which of the following is true? J sin(3x)sin(4x)dx = cos(x) – cos(7x) dx 2 ® Jsin(3x)cos(4x)dx = […

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Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 7. Prove: (a) sin iz = i sinh z. (b) | cos z|? = cos² x + sinh° y where, z = x + iy. COS

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Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

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Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

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Q: fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13…

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Q: In x 6- find lim + 3 + /3x dx 2 Jx 7- find 4 x, +x?)– Inx² -e In 99 dx | In(x 8- find (x+1) In°…

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Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.