1. Evaluate by using a contour integral method sins i) f'{- Vs

Q: Use Adaptive quadrature to approximate the following integral to within 10-5 ! (x + sin4x)dx 1

A: Given: The equation is ∫12x+sin 4xdx

Q: Evaluate the integrals ∫sec3 x tan x dx

A: To find the given integral.

Q: Use integration by parts to evaluate the integral: In(s)ds

A: Given, To Evaluate

Q: Ja (2) Suppose that F'(x) = f(x). What is the integral from a to b of f(x), with respect to x?

A:

Q: x sec (3x) tan (3x)dx

A: We use integrate by parts to solve the given integral.

Q: Evaluate the integral using integration by parts. Sxsin x sin (8x)dx Jrsi x sin (8x)dx =

A: Integration

Q: Evaluate the integral.  integral  cot  3 x  csc 4  x  dx

A:

Q: Evaluate the integral.  integral  sec 3 x  tan  4 x  dx

A: Given

Q: Evaluate the integral.

A:

Q: What change of variables is suggested by an integral containing Vx? + 36?

A: For, an integral containing  x2+36 we can change variable by substituting, x=6tanθ, As it will get…

Q: Use the Midpoint Rule to evaluate the integral fx sin(x)dx.

A:

Q: What change of variables is suggested by an integral containing V100 – x??

A: 100-x2

Q: Approximate the integral to three decimal places using the indicated rule. 308 -dx; trapezoidal…

A:

Q: Use any of the results in this section to evaluate the given integral along the indicated closed…

A: Cauchy’s Integral Theorem : If f(z) is an analytic function in a simply-connected region R, then…

Q: Evaluate the integral.  integral  cot  3 x  csc x  dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 3 tan (2x) sec (2x) dx

A: Given that: ∫3tan3(2x)sec5(2x)dx

Q: x sec (3x) tan (3x)dx

A: The given integral is ∫xsec3xtan3xdx. We know the integration by parts formula:…

Q: Evaluate the integral.  integral  sec 5 x  tan  4 x  dx

A: Integration:                    ∫sec5(x)tan4(x)dx                    Solving using Trigonometric…

Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

Q: Set up an integral that represents the arc length of the function y = 4x4 + 5x from the point (0,0)…

A: We have to find a, b and f(x)

Q: Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

A:

Q: Evaluate the integral.  integral  cot  3 x  tan 4  x  dx

A: Given :          ∫ cot3x tan4x dx

Q: 00 1 -dx x3 – 1 1 4

A: Use the definitions of improper integrals to write the improper integral in terms of limits.

Q: Evaluate the improper integral attached with this question.

A:

Q: to express the integrals as limits of [ f(x) dx (b) [f(x) dx

A:

Q: 4. fx√x - 3 dx

A:

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Evaluate the integral.  integral  sec3  x  tan  4 x  dx

A:

Q: sin x dx < 12 12 T/6 VI

A: Given π12≤∫π6π3sinx dx≤3π12 Here fx=sinx

Q: Prove by using integration by change in variable the ff. integral: dx = arcsec x +C xVx² – 1

A: Our Aim is to prove the given integral given below by using change of integration.∫dxx(x2-1)dx -(i)

Q: 4) Then, compute the surface area of the solid that is formed by rotating y = sin (x) [0, n] about…

A: To solve the following problem

Q: tan (5x) sec2(5x) dx

A:

Q: evaluate using the integral 34. tanx sec x dx II Expand

A:

Q: Evaluate the integral x tan x sec xdx (1)

A: We apply integrate by parts integration of fg'=fg-integration of f'g where f=x and g'=sec2xtanx.and…

Q: Evaluate the integral.  integral  cot  3 x  tan  x  dx

A: Given: ∫cot3xtanxdx

Q: If the substitution x = sin y is made in the integrand of . - A dx, the resulting 1-x integral is

A: Put value in  given  integral

Q: f(x)=sin(x)/x_between 0 and 1 using Trapezoidal

A: fx=sinxx Trapezoidal rule fx≈h2fa+2fa+h+fa+2h+---+fb a=0, h=0.05 and b=1

Q: Estimate the integral Sinx using Compostte tra pe zoidal rule with h=0.25

A:

Q: Evaluate the integrals ∫sec2 x tan x dx

A: Given:∫ sec2x tanx dx

Q: 1 dx = Jo 4+x

A: NOTE: Refresh your page if you can't see any equations. . ..............(1)

Q: 1 Oblicz d.x, Vax ах — х2 – x²

A: In this question, we have to evaluate the improper integral. Here we also use the property of Beta…

Q: determine Ahe impraper integral dx (H+1)(x²+1)

A: ................(1) use the partial fraction  ................(2) ................(3) take x=-1…

Q: Evaluate the integral using the substitution rule. 7/3 sin(x) dx cos?(x)

A:

Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Evaluate the integral.  integral  cot x  tan  x  dx

A: ∫ cot x tan x dx =?Used…

Q: tan"x

A: Integration: ∫x2.tan-1x dxWe need to put by parts formula    ∫uv dx=u.∫v dx - ∫[ddx(u).∫vdx]dx

Q: Evaluate the integrals ∫tan (ln y)/y dy

A: Given ∫tan(ln(y))ydy

Q: Fine the integral of sec ^4x tan ^3x dx

A: We  will  solve  the integral. We know, (1) tanθ = sinθ/ cosθ                (2)  Secθ= 1/ cosθ…

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.