sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

Q: sin(2n - 1)x sin nx If dx, then prove that sin x 2 sin x U -U, =: -1, =U and find 1, = 2

A: The expressions are Un=∫0π2sin2n-1xsinxdxtn=∫0π2sin2nxsin2xdx We have to prove,…

Q: u= - e' sinhx satisfies one of the f ollowing u = -u O"xx Not harmonic Harmonic u =u O "x

A: U is not harmonic

Q: Verify the identity:

A: The given identity is sin3x+cos3x=sinx+cosx1-sin2x2

Q: sin x+cosX Differentiate y = %3D sin x-cos x 2 А. 1-sin 2x -2 В. 1+sin 2x -2 С. 1-sin 2x 2 D. 1+sin…

A: Given,  y=(sinx+cosx)/(sinx-cosx)

Q: sin' y 10. lim y→x 1+cosy

A:

Q: sin 0 lim 0lr tan 0 O a. 0.5 O b.0 O c. 1 O d. 1

A:

Q: (sinx E,x# 0 a) f(x) = in x = 0 0, x = 0 b) f(x) = x - |x| in x= 0

A: Topic:- Continuity

Q: sec 3 x tan x (sec ³x sec³x secrx S see of secxu S u ли secx u du dx let a = tan x du = sec² x dx…

A:

Q: x + y x - y cosh Show that sinh x + sinh y = 2 sinh

A:

Q: sin(4-y)sin(3-y)dy

A: Use the formula sin(A) sin(B)=12(cos(A-B)-cos(A+B))Consider…

Q: (sin 0)y" - (cos 0)y' 2 %3D

A: In the given question 5, The order of the differential equation is = 3 And the equation is linear.

Q: いpO O siniz iff Z-kTi,K-o,っ3リーー Sin iz ニ

A: we have to prove that siniz=siniz¯ if and only if z=kπi, k∈ℤ.

Q: sin(2n – 1)x dx , Un %3D sin x

A: Yghhhhhhg

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

A:

Q: sec e de 1+ tan 0

A: To find∫secθ1+tanθdθ

Q: integrate (cos (x)/(sin(X)-cos(x))

A: Integration is a technique of finding a function  the derivative of which, , is equal to a given…

Q: sine 2. Co s+1 J9-x2 5. 5 + x² Q4 メP 2.

A: Please refer the attached image for complete solution. Given: four integralsTo calculate:…

Q: (1-cos 6x)dx 1+cos 6x c. tan3x – x+ C Perform the integration:S A. tanx – x + c B. -tanx – x+ C 3 3…

A: To find given integral.

Q: sin 2x 4. tan x = %3D 1+cos 2x 19 5. tan %3D = CSC X - cot x

A:

Q: S(csc x cot x + 7x°)dx O sin x – x' + c O cos x + x7 +c .7 O cot x + x' + c tan x + x' +c - csc x +…

A: To integrate.

Q: sin(2n) 1+/n In %3D

A: Write in product of two sequences

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: siny dle = (1-x cosy) Cas y

A:

Q: Antiderivative of sec(3x)tan(3x)

A:

Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: 3. Double Integration Evaluate the equation below sin 0 r3 cos 0 dr d0 0. 브2

A:

Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: sec (0) J de 5-sec2(0)

A:

Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

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Q: Cycloid arch: x = a(0 – sin 0), y = a(1 cos 0) - -

A:

Q: sin' x Evaluate : dx (1+cos x) 1+ cos x+ cos* x 1+ cos x)1+ cos x+cos cos' x

A:

Q: fy=sin-¹ find Zy

A:

Q: CO SK= Sin X CoS X イメそ2 X= 2anctgt Sin X+ CosX dx= dt 5inイミ イet? ュラナと 2t と? イ2 2dそ (て ーそス 2そ+イーそ?…

A: The function is, ∫sinxcosxsinx+cosxdx

Q: Cos ly -A) %3D show that 2 ニ0 2 8x Sx8y

A:

Q: A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

A: The given function is: f(x)=xe-x ,      x>0

Q: 24 dx Evaluate 1- cos (8x) 24 dx 1- cos (8x) %3D

A: We have to find the integral of given function.

Q: 6 sin° x+ cos° x dx sin xcos x Evaluate :

A:

Q: sin- In?| 4+ tan-'cos- dx 2 COs- 1+ cos 4+ tan-'cos In2 4+ tan-'cos- dx 2 2sin- 2 (A) 4+ tan-'cos- 2…

A:

Q: sec x-1 sin x %3D secx+1 1+cos x

A:

Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: sin'x cos'xdk 3. X COS

A: It is given that, ∫sin2xcos3x dx We have to solve it.

Q: 3 sinx+cos x Evaluate S dx. 2 sinxcos x

A:

Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

A:

Q: Arcsin (0.48). 0.02 а. V0.75 0.02 + b. 6. V0.75 0.02 с. п- V0.075 0.02 d. π V0.075

A:

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3D cOS x 1+2y + cos x-sin x 1+ sin x 1+ 1+ cosx 8.…

A:

Q: sin (x) dx (2+3 cus(x))² 3(2+3 cos(x)) с

A:

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3| cos x 1+2y + cos x- sin x 1+ sin x 1+ 1+ coS x…

A: Introduction :

Q: sin 0 sin 0 2 1- cos 0 1+ cos e tan 0

A:

Q: 1+sin A cos 2 sec u – cos µ = sin µ tan µ 4. + 2 sec 1 %3D cos A 1+sin A

A: We have to verify the given identities.