Evaluate the integral. 7U/4 O 10i+ O [(10sect)i-(3+ sin t)j - (2sec t tan t)k)]dt (2√√2-37-4) 2 10i+ O (2√√√2+3π+4) 2 10i+ (2√√2-37-4 2 (2√√2-37-4 4 101 + + [2√2-1 j+2(1-√√√2)k j+2(1+√√2)k j+2(1+√√2)k j+2(1-√√2)k

Q: (b) Show that i³i is real, even though i or 3i is not.

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Q: Jx sin 8xdx is O a. -xcos 8x sin 8x + 64 O b. - xcos 8x sin 8x 8 64 O C. xcos 8x sin 8x 8 +c 64 O d.…

A: ∫x sin8x dx On integrating by parts, we get ∫x sin8x dx=x·∫sin8x dx-∫dxdx·∫sin8x dx…

Q: Integrate using the method of trigonometric substitution. Express the final answer in terms of the…

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Q: a) 2 cos x - √√3 = 0

A: a) The general solution of  cosx=cosα  is  x=2nπ±α    where , nϵZ  in given question, 2cosx-√3= 0…

Q: TV2 a cose r √ a² + r² dr do

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Q: What is the argument of the complex number given by z = (1+ iv3)(1 + i)(cos(0) + isin(0)) Select…

A: We have to find argument.

Q: Express as a product. 2π 2π sin (a - -) - sin (a + 3 3 -)

A: given expression

Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

Q: d 3. Evaluate (r“ + 4° + VT+ 1 + sin(4)). dx

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Q: (15t-2 – 5t) cos (6t-1+t²)

A: using substitution method to find integration

Q: (b) Let A1, A2,, A46 be the roots of (5 – 2i)/46. Show that 46 II ^.A; = = 29 i=1

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Q: Express as a product. sin (a- - 2π 3 - -) − sin (a + - 2π 3

A: The given expression can be expressed as a product :     sin(α−32π​)−sin(α+32π​)…

Q: Evaluate e cosh 2t -3t s13 d) 4(s? - 6s-5) 3. s43 a) 4(s-6s + 5) b) 4(s? + 6s - 5) c) 4(s + 6s +5)

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Q: Evaluate D 6 |3x|√9x²-4 3 2 sin-¹3-sin-¹ 3 tan¯¹3-tan -1 1²/24 sec ¹3-sec dx sec-1³/12

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Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: b) Prove that, S∞ (@3x+1)² dx e2x 2π 9√3

A: Let we get, Let We get, This implies, This implies

Q: 2. Simplifying complex rationals 1 1 2xy 3 a) 4 4 3 b) гу? T

A: The solution is :

Q: 6. Find Arg 2 1+√3i arg(-1+√3i)· 7. Write the following complex numbers in rectangular form. (77)…

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Q: 88 11% COSX + dx cakulate using complex functions?

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Q: sin –9xdx

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Q: Use the formula d = √² +²2-2r₁ r₂ cos (0₂-0₁) to find the distance 3π between 4, 4 and 8, T

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Q: What is the value of x? √2 cosx-1=0 2sin3x+1=0

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Q: 4x A. dx - 3 4 4x A=²³cof=1¹³) + C__ _B. — co(=^^) + C +C 4 4x c. ²2 cof=14) + C 4x D.= co(-1) +

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Q: Write the standard form of the complex number 4(cos(4π÷3)+isin(4π÷3)    Find the product:…

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Q: 3[3°-2ャ

A: We can find the answer using BODMAS rule as below

Q: Simplify the complex number 7 (²+1) ³ - 5 (¹)² and express it in the standard form.

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Q: Use substitution to evaluate sin2x√/4+9sin²x dx A (26/13-16) B 27(26√/13 (26√/13 – 16) C 27/7 √…

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Q: Evaluate the following: (Complex Numbers & Variables) 1.) √j√j

A: