Prove that S. 8 dx √π 2

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Q: press cos x √3sina in the form of Asin(x − a) with 0 < a <

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Q: (Sinx) (xl (X+3}*

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Q: da Evaluate x² V4

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Q: c2π 0 cos 2t 17 - 8 cost dt

A: Cauchy residue theorem is used to find the integral of a closed curve. Cauchy residue theorem says…

Q: 7. Evaluate. LL sin z da dy.

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Q: 3) Prove that x 20-1 1+x2 dx C ال 플 CSC (Jia)

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Q: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

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Q: The sec√x dx is {A}=sec x³/2 + C {B} ²sec ³/2x + C 3 {C} 2 In sec √x + tan √x {D} In sec √x + tan √x…

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Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: c2π cos² t 13+ 12 cost dt

A: The Cauchy Residue theorem is a part of the complex analysis. By using the Cauchy Residue theorem we…

Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

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Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: 1. In section 5.8, we saw that f du = tan-u+ C. Use a u-substitution, then this formula, to u?-…

A: topic - indefinite integral

Q: de − 7 √(1-k² sin²0) 2F₁ ( ½ ‚ ½ ; 1;^²), \K[<1

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Q: $ S®- floor't. & сод

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Q: 8 dx sec 2x-1

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Q: 3. Find . a. y ( +2r + 10) cos(r)

A: Find the derivatives of the given functions. Use the derivative formulas:…

Q: Compute at 0 = 0. de [tan (20) + 04]

A: here we have to find the differentiation.

Q: 6. f cos³x√sin xdx)

A: sin2x+cos2x=1∫xndx=xn+1n+1

Q: Prove 2- = =4 has infinite many Solu thans ZEC.

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Q: Evaluate the definite integral 8 | (18a? – 8x + 3) da

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Q: 2. Prove that fo So dx=3(2-√2)

A: We need to solve integration problem.

Q: Solve the integral 10. (tan 2x + sec 2x)³dx

A: Given integral is: I=∫tan 2x+sec 2x3dx We have to find the value of this integral.

Q: sec−π/3

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Q: Show that 9 √ √5 + 4x − x² dx - sin-¹)+(x-2)√5 + 4x − x² + C. =

A: Here we have to solve the given integral.The given integral is ∫5+4x−x2dx.

Q: gg Un= 0 1- Cos nn dr 1- Cosit Unt₂ + Un = 20 ot prove that

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Q: 5. Find dy dx of √xy + 2x = √√√y

A: Topic = Derivative

Q: 3. Show that Hence find x¹ - x² + √√x X x³ = x+x==²= P - [ 2² = 2² + √² dr. X

A: We need to perform integral.

Q: 8) Evaluate So (x-1) dx Dod

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Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: 4. [ sin* r cos* adr

A: Given integral:- ∫sin3xcos5xdx

Q: determine if the functions are one to one y = √36-x², y = = = ² 2 y =√x+1 − 3 1

A: A mapping f: A→B is said to be one-one if for each pair of of distinct element of A, their f are…

Q: +1- 2 cos 0 for Z E C., show z"+ = 2 cos(n@) that %3D

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Q: 니.1 Find the Sum 40 2:(31-1)

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