the point of discontinuity on(0, co), the Fourier Sine integral converges to: None (**) + f(x¯)] **) + f(x )]

Q: 4) In each part, determine whether the integral is convergent or divergent. 5 3 D 00 √x dx b) 0 - dx…

A: Solution to the integrals.

Q: "S". If f(x) is continuous and f(x)dx = 2, then: x/4 3 ** sec²(1)ƒ (tan(1)) dt =

A: dtantdt=sec2ttan(0)=0tan(π4)=1

Q: Compute the integral ff x cos(xy)dA, where R = [0, 1] × [0, π/2]. R

A:

Q: 4. (5pt) If f(r) = [t – 1) cosh t dt, on what interval is ƒ increasing? (Hint: Use the Fundamental…

A:

Q: 2 4x 1 3 x2-4 dx

A:

Q: solve integral eqn. use L.T. and Convolution Integration 0 to t ( y(x)/(sqrt(t-x)))= 1+t+t^2

A:

Q: Exercise 1. (a) Prove (using direct proof) that Vn € {odd integers}, 3j € Z|n = 2j - 1. (b) Write…

A:

Q: Sketch the graph of y = 4-√9-2² over the interval [-3, 3], and use the notion of net area to compute…

A: The given curve is:

Q: Write the following expression in algebraic form: sin(arccos (6x)) V1-36z2 O VI – 36x² O VI – 6x² O…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Estimate the integral of f(x)= x2- 2x+4 with unequally spaced points xO= 0 , x1= 0.1 , x2 =0.3 , x3…

A: Note : X4=1.0 in the problem since a data point appears only once in the table.

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: Show that for k>0 and c>=0, ln(n^k+c) is big theta of ln(n).

A:

Q: Consider the improper integral Justify your reasoning. (a) dr. Does it converge or diverge?

A:

Q: Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w…

A:

Q: Express lim,00 E= cos( + ) in integral notation. i=1 _2n

A: Since, the above equation is given in the form of Riemann's integral, which is given by-…

Q: show that (2n+1) Pr= PA+t=PAt Use tege ndre palgnanicds the

A:

Q: An odd piecewise continuous function f(x) on every finite 00 interval of (-0, x) such that \f(x)|…

A:

Q: (b) Find the value of each convergent improper integral and show why each divergent improper…

A: We need to calculate the improper integrals and then conclude it as convergent or divergent.

Q: A(t) = 3000e027z initial investment of 3000 dollars which pays 2.7% compounded continuously. a) Find…

A:

Q: The tangent line to the graph of some function f at x = 4 is y = - 2x + 5 corresponding normal line…

A: Given query is to find the equation of the normal line.

Q: Use (3) from Section 5.4 to evaluate the integ '5 x-7/9 –7/9 dx

A:

Q: What is the total change of f(x), if f'(x) = cos(2.5x), over the interval [0, π ]? -1 -0.4 0.4 0.6

A: The derivative of f(x) is

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: How do I do this one?

A: Given integral is The integral is improper and can be evaluated as follows

Q: f(x)=0.2+25x-200x² +675x³-900x¹ +400x³ a=0 ve b=0.8 a.) find the integral by using Simpson 3/8 Rule…

A: Concept: Simpson's rule: One of the numerical approaches for evaluating the definite integral is…

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.