a) Evaluate the integrals using appropriate substitutions. dx Sine i) S ii) S de Cos? 0+1 1+16x?

Q: cos(8) cos (sin(0)) de

A:

Q: Evaluate the integral. cos(z) dz sin? (z)

A:

Q: Use a double integral to find the area of the region. The region within both of the circles r = 6…

A:

Q: 4 sin 3y–6 dy cos 3y

A: We'll evaluate the integral as following.

Q: me result of the integral in 0 given | V ²– 25 -dy is 5 tane – 50 +C , y A) True B) False

A:

Q: Write the integral S Li dz dy dx in the form dx dy dz. Do NOT evaluate the (2) integral.

A:

Q: 3. What are the integrals of tan x and cot x? sec x and csc x?

A: Part (a) - Let the integral be y - y = ∫tanx dx  y = ∫sinxcosxdx…

Q: dy 1+ sin 4y

A:

Q: Evaluate the integral. cos y dy sin 2y + 2 sin y – 3

A:

Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: S(cos 3x + sin 7x)² dx

A: Here, when we solve this integration it becomes separate integration of trigonometric term and…

Q: Evaluate the integral. 9 dx V64 - Sx2 sin +C tan sin +C tan +C a eo

A: To evaluate the integral

Q: r430 sin x 160 cos2 x(16-sec² x)

A:

Q: Which integral represents the length of the curve y = cos x be- tween 0 and ? I V1 + cos? x dx, I…

A: the given equation of the curve is: y=cosx we have to determine which integral represents the length…

Q: [? sinycos° ydy 2

A:

Q: use a geometry formula to find the exact value of the definite integral  4x dx on the interval [0,b]

A: The given function is 4x with the interval [0,b].

Q: sec(2) tan(z) – 1 dz 1 dz

A:

Q: 52. Use the substitution u = tan x to evaluate the integral dx 1+ sin? x

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Q: |a" cos(2°) da = +C. %3D Hint: First make a substitution and then use integration by parts to…

A: Consider the given integral ∫x11cosx6dx. Let u=x6. That implies, du=x6dxdu=6x5dxdx=du6x5 Then, the…

Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=; , to approximate the integrale-2x²…

A: Note:- As per our guidelines, we can answer the first part only as both are different and first part…

Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Evaluate the integral using the given substitution. 15) 1- sin cos dt, u = 1 - sin 13 1 - sin + C A)…

A:

Q: Find the area inside the cardioid r = 4+ sin0 from 0 = 0 to 0 = 2n.

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 4x² – 25 7. = sec 0 dx

A: 7) a)Evaluate the integral using the indicated trigonometric substitution. b) Sketch and label the…

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: Use the fact that cos(z) = R(eiz) = (eiz + e-iz)/2 to find the integral of (e3xcos(4x))dx.

A: Here the given integral in not in the complex form so we calculate the integral as it is given in…

Q: Sa cosxcos(sinx)dx

A:

Q: Evaluate the definite integral. 2exin ( z ) cos(z)dz 0.

A:

Q: Evaluate the integral. S (sec z ecr tan r + sec² x) dx

A: For detailed solution see the next step.

Q: S sin y cos('/2) dy

A: ∫sinycosy2dy

Q: Use a double integral to find the area of the shaded region. 7/2 20 r= 9+9 cos e 10 - 10 -5 5 10 15…

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Q: Sketch and evaluate the reverse integral 3. dy dz

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Q: Transform the integral fo So? sin o sin 0 do do by the substitution r = sin o cos 0, y = sin o sin 0…

A: Given ∫0π2∫0π2sinϕsinθdϕdθand x=sinϕcosθ, y=sinϕsinθ

Q: 2. Calculate the integral , sin(x²)dx by the Gauss quadrature with n+1 = 2 and 3 quadrature points.…

A:

Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: pts Evalaute the integral y sin(z) dz dy dz. Enter an exact answer using fractions and radicals as…

A:

Q: The suitable substitution to evaluate the integral (V cot (2x) dx is sin (2x) Ou3tan(2x) none Ou=…

A: To find The suitable substitution to evaluate the integral.

Q: By using trapezoidal rule, n=2, The integral J = 0.9444 0.9480 0.9481 O 0.9482 O 0.94809 π/2 0 sin…

A:

Q: Determine a definite integral that represents the arc length of r = 6 cos(0), 0 <0< de 0. 下一2

A: Arc length

Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

A:

Q: Use the trigonometric substitution r 2 sin 0 to compute the integral -2 VA – r² dx

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Q: Evaluate the iterated integral. 5x 15x? sin y dy dz dx Jo

A: Given ∫0π∫05x∫0xz15x2sinydydzdx Evaluate the iterated integral

Q: 3. Approximate the integral using: (a) (b) 11 trapezoidal rule. Simpson's rule. 0.8 [8 dx

A:

Q: 3(sin y- cos y) chy cos y

A: First we use (siny - cosy) 2 =sin2 y + cos2 y -2sinycosy Then using u substitution let u =sexy +…

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral  tan 3  (  1/z)…

A: To integrate: ∫tan31zz2dz Let substitute t=1z Differentiating both sides, we get dtdz=-1z2-dt=1z2dz…

Q: Evaluate the integral fo S (y co W COS + 2) dydx.

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Q: Use a double integral to find the area of one loop of the rose r = 2 cos(30).

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Q: Complete the integration: Ssin (x)cos (x)dx = sin (2x) sin (2x) + C ? %3D 16 32 Determine the yalue…

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Q: Evaluate the integral I = x + cos()dx using two point and three point Gaussian Quadrature and…

A: We have I=∫-11x2+cosx2dx First, we find the exact solution. Consider:…

Q: 7/2 VI- cos z dy dx dz

A: The detailed solution is as follows:

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.