d du 1) dx [sin-1u] = %3D 1-u2 dx -1 du 2) [cos-1 u] = dx %3D 1-u2 dx d. du 3) [tan-u] = %3D dx 1+u2 dx

Q: 2. 1= j tan(4x³) ,sec²(4x²)xdx dx 1- I=31-2x) (In( 5. I= 3. 1= ftan? (3x) sec? (3x)dx

A: Here we have to find the value of the following integrations. Note :   As per our company guidelines…

Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

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A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

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Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

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Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

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Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

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Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

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Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: dt cos (2 sin 21) /1– 4r

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Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

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Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: -1 du 4) [cot-u] %3D 1+u2 dx dx d 5) 1 du [sec-1 u] %3D dx u vu2-1 dx -1 du 6) [csc-1 u] dx u vu2-1…

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Q: d du 1) (sin-1u] dx %3D 1-u2 dx -1 du 리는 [cos-1 ul = dx V1-u2 dx d 1 du 3) = [tan-1 u] dx %3D 1+u2…

A: I have solved first three part for other repost question

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

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Q: dy dx a) { In |0* + 1|} „b) arctan (ve2 -1) , c) sec-(0²) – 1

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: Evaluate the integrals

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

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Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: 1.) Evaluate In 2 e*2arctan e* J (1+ e2x) sec(2arctan e*)' А.) -dx. ežr(1 – e*r)- (arcsin e 2x) cos²…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

Q: Let 3 sin x + 7 cos y = 3. dy %3D dx d²y dx?

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Q: If y = (sin-' x)², show that (1 – 2*) dy dr? dy 2. dx

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Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: _5. In the equation y = sin-1 x, if = , then y= TC %3D %3D %3D

A: 5. In the equation y=sin-1x , if x=12 , then y=π6. The given statement is True, The reason regarding…

Q: 4 sin' 2x cos 4x dx 4.

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Q: 1- Sinx + Cos2y=0 dy dx

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

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

A: We have to proof

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Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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