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

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: (d) | Ta2 – 4)3 dx -

A: To Determine: Convert the indefinite integral into definite integral using the interval [0,1]…

Q: Show that d (x + 1)? 1 (을 tan 'x + t In dx (1 + x)(1 + x²) x? + 1

A: The given function is

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

A:

Q: The smallest positive, nonzero root of cosh x cos x - 1 = 0 lies in the interval (4, 5). Compute…

A:

Q: rin 2 e2# sec-"(e")dr

A: Solution

Q: Compute the following integrals given that  ∫∞-∞ |f(x)|2dx =  ∫inf-inf|f^(s)|2ds: I)…

A: solution is given below:

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

A:

Q: 3. [20 points] Calculate the integrals: (a) (b) |(2+ 4)(2r – 1)dz (c) (d)

A:

Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

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: f(t) = 3/256 t^5-23/16 t^4 + 3945/64t^3-8695/8t^2+7176t+2500 g(t) = 2000 Cos ((11/105) t)  +8500…

A: We are given that f(t)=3256 t5-2316 t4 + 394564t3-86958t2+7176t+2500 and g(t)= 2000 cos11105 t…

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

A:

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: 5. 0 sin² x x² + 1 xp

A:

Q: Express lim {5(x;)* – 6 tan°(x;)}Ax, n-+00 definite integral over the interval [-3,2n]. as a

A:

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Use substitution to evaluate the integral in terms of f(x). Choose the correct answer. f'(x) dx =…

A: To evaluateI=∫f'xfx dx

Q: Q/5 Evaluate the integral of: (a) St³et* dt dx (b) 2 x (In x)²

A: We have to evaluate the integral. Using the substitution method we can solve these questions.…

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: the integral of (15tan-1(x))/x2

A:

Q: f(x) is continuous on (- 0,00). Use the given information to sketch the graph of f. f(-3)= 0, f(0) =…

A: Given table:-

Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

A:

Q: Evaluate the definite integrals a) (бх? — - 2x – 10) dx = / (x+ 4)² dx = b) 1 c) (x* – x³ ) dx - ||

A: Some of the properties of integration  ∫abf(x)dx=F(b)-F(a) ∫xndx=xn+1n+1+C…

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

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.