1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

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: T² 2 / (x + 1) (2² + 1) dr. Evaluate

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Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

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Q: sec x=1/5 on [0,2pie)

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Q: Evaluate f x'V 1+4x² dx.

A: Consider the definite integral ∫01x21+4x2 dx to evaluate this, first evaluate the indefinite…

Q: 24. By Simpson's rule, evaluate Vi – 1/x dx with fiye ordinates

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Q: Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In…

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Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

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Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

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Q: 1. (a) Evaluate Jo 0 r* - ¹ (1 − x6) 15 (1+x) ¹5 -dx.

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Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: Evaluate. 3 Lox f(x) dx, f(x) = (−x + 1, x≤2 1-x² + 6x-9, x>2

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Q: 9. f 6 sec¹ xdx

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Q: 10 6. Evaluate -dx. (x – 1)(x² + 9)*

A: Given integral is We will evaluate the integral by using the concept of partial fraction…

Q: y=ー-x+5 3 y=-x+7

A: This question is based on Substitution.

Q: Differentiate. y= In [(x+7)* x + 8)®(x +2)°] dx

A: Given y = ln(x+7)4(x+8)6(x+2)3

Q: x sin x Evaluate the integral dx using residues. (4 + zX)(I + zX)

A: Given ∫0∞xsinxx2+1x2+4dx=imaginary part of ∫cRfzdz Let, fz=zeizz2+2z2+4 Singularities of  fz where…

Q: 7/2 79. Prove that 0< sin x dx < Ja/4

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Q: 1) Prove that for any space, X, with any topology, T, that: (i) CI(X) = X and (ii) Int(X) = X.

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Q: 6. dx = x + 4x + 5 (A) arctan(x + 2) + C (B) arcsin (x + 2) + C (C) In|r*+ + 4x + + C 1 (D) + C x° +…

A: Proceed as shown below...

Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: /2 Prove that 5x1² |π x J1,2 (2x) dx = 1.

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Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy),  xy ≠ 1.                   Use the…

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Q: 2. Use partial differentiation to approximate the following sum, not the individual radical. V81 +…

A: According to question,Given expression,81 + 263

Q: 1 + x² · dx + x3 1 + x? dx (1 + x)³ 121. 122. [Vi+v 123. / Vr. Vi + Vx dx 124. /V1 + Vī + x dx + V1…

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Q: 1. Evaluate [(2sin 2x+3Tanx – 5 e-5* +4x' -7) dx .

A: Integrate each term

Q: Integral 1. xp x²(x - 1)

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Q: X -₂(x - 2)(x + 3) -2 dx

A: given