3. [ (sec²(a) — csc²(a) + π) da

Q: -11sin (z)dz -

A:

Q: L[sih bt) 2.

A: From the definition of Laplace, L(f(t))=Fs=∫0∞fte-stdtSo,L(sin(bt))=∫0∞sin(bt)e-stdt Let,…

Q: Find the Principal Value of (-2)i/π.

A: We find the Principal Value of (-2)i/π.

Q: Evaluate. [16si 16sin-4x cos³-4x dx

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Q: 1. Find 2(3z + 4)² dz.

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Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: oB coser sec 2o -

A: To find the value of 2cosec20°sec20°

Q: 2.) ( 4x - 29x- 38) ÷ ( 2x + 3 )

A:

Q: c. Show that(cscx) -1 xVx2-1

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Q: S 2sin(4x +9)dx

A: Given query is to find the integral ∫ 2 sin(4x+9)dx.

Q: 6х —9 4.) dx 22— 3х +2

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Q: 9 = dy

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Q: 5л — 2 dx x2 +1 10.)

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Q: хt — х +6 dx х3 + Зх

A: We shall use polynomial long division method to simplify our integrand.

Q: √(x³ + 2x² + x -5) e 2X dx

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Q: (1 + 1)e dr 5.

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Q: Find the reciprocal of (1.5 + j2.5)

A: The given complex number is 1.5+j2.5 This can be rewritten as 1.5+2.5j The reciprocal of the given…

Q: Find the real values of x and y such that (x + iy)2 = -8 + 6i.

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Q: 1. Find a b (a) a =, b = (b) a =, b = (c) a= 27 +3j - 4k, b = i-3j+k

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Q: (1 +i)(13 – 4i)(1 - i)

A: We have to simplify the given expression: 1+i13-4i1-i We know that a+ba-b=a2-b2i=-1i2=-1 Where, i is…

Q: = (2xy + z² )i + (x² +z)j + (y + 2xz)k, determine a possible value for .

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Q: Exc. Eind. Lim (x-1) y3

A: Solution:

Q: Calculate  x and y (2+xi)+(y+3i)=7+4i

A: Complex numbers are those numbers which is represented in the form of (a + ib) where is a real part…

Q: (c) f cos³ 4tdt

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Q: 1 da (2a + 1) +1) 1. 8.

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Q: (cos-¹2w) 6. ¡ COS dw √1-4w²

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Q: Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

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Q: 3[3°-2ャ

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

Q: b. 3+V5-x 3I

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Q: 3x Evaluate x² +¹+e³ª)dx.

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Q: b) 2(x4+1)5 dx

A: