Find all the numbers z such that e^2iz= 5i.

Q: . Find EY.

A:

Q: S(7x-2)³ dx = (7x-2)4 + C. 28

A: The given integral,      ∫7x-23 dx=7x-2428+C

Q: Use FTC I to show that x" dx = 0 if n is an odd whole number. %3D Explain graphically.

A:

Q: Find the indefinite integral ∫tan6 3x dx

A:

Q: 9. tan 2x dx 5.

A: Given: ∫0π6 tan 2x dx To solve: The given integral.

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: A number of the form iy is called pure imaginary

A: A number of the form z = x + iy is known as complex number, where x is real part and y is imaginary…

Q: Use De Moivre's theorem to solve:

A: Given,  x4-1+i=0

Q: Integrate the square root of (1 - sin² x) dx.

A:

Q: Find the thickness x of the hollow cylinder of height 100 cm if the volume between the inner and…

A: Given:- Here, a hollow cylinder is given. The thickness of the cylinder is x Height is 100 cm The…

Q: find integral tan 5 x sec 7 x dx

A:

Q: 5. 12 sec² (3x) dx 0.

A: We have to solve

Q: the integral of sin5(2x)cos4(2x)dx

A:

Q: solve for t

A:

Q: Find two z values so that 48% of the four decimal places, separated by a 0,0.

A: Given Data: Z is the standard normal distribution   P(-x<z<x)=0.48 P(z<x)=0.74

Q: 2x d tdt da

A:

Q: determine the integration c Sinx

A:

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: find integral sqrt (1 - 4x 2 ) dx

A:

Q: find integral 1 / sqrt ( 9x 2 +6x - 8 ) dx

A: Given: I=∫dx9x2+6x-8 for evaluating given integral, first we convert given integral in standard form…

Q: Evaluate: ³4₁ [2³(x + y)³] dz dy dx

A: To evaluate the given integral.∫-43∫-12∫01z3x+y3 dz dy dx

Q: vx +1 Sinh Cschx = In 671 %3D %3D

A: First, let us evaluate sinh-1x.  Let  sinh-1x=zx=sinhz It is known that sinhx=ex-e-x2 Therefore,…

Q: Find root √80 using Newton Raphson method.

A:

Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: min

A: We have to find the following given integral according to the given information

Q: (2 + j)?

A:

Q: Integrate with respect to x, the square root of (1-cos5x)/2

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Q: - х e con 2x dx

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Q: Evaluate the definite integral. rề arcsin (3x) dr VI - 9.x2

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Q: | (о + 1) In (») da

A:

Q: sec2 X dx 3

A:

Q: use a geometry formula to find the exact value of the definite interval square root of 16-x2 dx on…

A: The given can be consider as a function,

Q: Bring out the importance of Frii's formula.

A: Answer: For the given data

Q: Use an appropriate substitution to integrate 24xcos(x2-2)dx

A:

Q: Solve for Fourier coefficient, f (x) = Ssin x 02x2n T >x 22n

A:

Q: find integral  sqrt ( x2 - 9 )dx

A: Given: I=∫x2-9dx we know that ∫x2-a2dx=x2x2-a2-a22lnx+x2-a2+c                                ..1

Q: Find the general solution of the ODE.

A:

Q: Use FTC I to show that x" dx = 0 if n is an odd whole number. Explain graphically.

A: Given: show that ∫-11xndx=0 if n is an odd whole number we know that  ∫xndx=xn+1n+1+c…

Q: Jz sin 0 do 2

A:

Q: sin* 30d0

A: Expand sin^4(3theta)

Q: Determine the following indefinite integral.

A:

Q: dx 2/3 Thtegrate -27 3)

A: Given: ∫-278dxx23 To determine: The value of given integral. Formula used: ∫xndx=xn+1n+1+C

Q: 2°(5 - у)' dy

A: The given integral is: I=∫2y(5-y)3 dy

Q: / log, (x2) dx

A: According to the definition of the logarithm, if y=ax, then logay=x. The logarithm with base e is…

Q: Find integral 2  to 5    1/ sqrt  (x -2 ) dx

A:

Q: find integral tan 6 x sec  4 x dx

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Q: how that 1 dn v2

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Q: 6. tan (9x + 5) + C 1. O B. - O A. sec2(9x + 5) Which function should be differentiated? 6. tan (9x…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.