Using transform, find the result of the integral x = 3rcos(0), y = 8rsin(0) LL dxdy 0.

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: Use U-Substitution fo evaluate the integral,

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Q: Find the area bounded by the parabolas x2+y-9=0 and x2-8y=0   (SOLVE BY USING INTEGRAL CALCULUS)

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Q: (c) Evaluate * sec x tan x dx using the table of standard integrals.

A: a) i) It is required to find ddxetanx. Differentiate etanx with respect to x. ddxetanx=etanxddxtanx…

Q: ln (ale) secx (2– sec²x)em sec(3A – x) What should be the value of A for dr to be integrable using…

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Q: Using integration, derive the Laplace transform of: * L(sinh at)

A: This is a problem related to integration. based on the general formula and concept we will answer…

Q: Evaluate the integral. show that it is divergent.  integral  x 2   - 2  x dx

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Q: dx Use the Substitution Formula to evaluate the integral x(Inx)*

A: The given Integral is ∫24dxxlnx2

Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A: The given line integral is ∫c-ydx+xdy along the curve c: y2=6x from (6,6) to (0,0)

Q: Evaluate the integral. (Use C for the constant of integration.) (x2 - 9x) dx

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Q: a) Evaluate the indefinite integrals using Repeated Integration by parts i) fx²e-2*dx ii) fx?Sinxdx

A: We have to evaluate the given integration.

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

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Q: use integration by parts to establish the reductionformula.

A: Integration by part formula: ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Using R, apply Monte Carlo integration to estimate the following integrals: -x2+x dx

A: Monte Carlo integration uses a set of random points in which the area under a curve is computed by a…

Q: dt t²-t+2 Find the integral of S-

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Q: 00 1 (b) Calculate the improper integral dx , or show that it (x² + 25)3/2 -00 diverges . Show your…

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Q: Find dx -4t dt using the method indicated. a. Evaluate the integral and differentiate the result. b.…

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Q: Givm trapgoidal rule with h =0.25 by Using apploximate the integral.

A: The solution is Given as

Q: O Use differentials to approximate the increase in the area of a soap bubble when its volume…

A: Given query is to find approximate are increased.

Q: S Vtan x sec“(x)dx Evaluate the integral a

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q:4) Evaluate the line integral of the function p(x.y)=y-x,over the straight line Joining the two…

A: Function p(x, y ) = y - x   points ( 4, 0 ) and ( 0, 4 )  To Evaluate: Integral  of the given…

Q: -Ixl dx Find the value of the integral and determine whether it is divergent or convergent

A: The given integral is ∫-∞∞e-xdx. Calculate the value of integral and determine whether it is…

Q: Using Variations on the substitution method Find the integral

A: To evaluate integral ∫xx+1dx Let x+1=t Differentiating both sides with respect to x,…

Q: /Use Simpson rule to evaluate the value of integration F(x) dx for n 4 -1 6. 6. 825 8 F(x) -124 -52…

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Q: b) Evaluate the indefinite integrals using Tabular Integration by parts. i) S(x² + x + 1)Sinxdx ii)…

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Q: sec?x dx 1- tan x b. Determine whether the integral converges or diverges.

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Q: Use integration by parts to find the integral. (7x-3) e-2x dx -2x dx = (7x-3) e

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Q: R; Being the 1st region of the coordinate plane between the y = x line and the y=x² parabola,…

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Q: S x² e¹x dx

A: EVALUATE USING INTEGRATION BY PARTS  For the function x2e4x .

Q: dx: Evaluate the improper integral if it exists The improper integral diverge:

A: ∫1∞1x3dx=-1x2

Q: Determine whether the improper integral converges and, if so, evaluate it.

A: ∫56dxx-532 On integrating, we get ∫56dxx-532=∫56x-5-32…

Q: Use integration by parts to evaluate the integral. (Use C for the constant of integration.) In(5x)…

A: Given , the integral We have to evaluate the integral by using by parts formula.

Q: 1 On3º do

A: Recall: ∫axdx=axln(a)+C integration by parts: ∫udv=uv-∫vdu

Q: Use the Integral Comparison Test to show that dx diverges by comparing with the integral Vr +1 1 dx;…

A: Integral comparison test:  Let fx and gx are continuous function for x≥a and fx≥gx≥0 for every x≥a.…

Q: Using integration, derive the Laplace transform of: L(cosh at)

A: We will use the definition of laplace transform and concept of definite integration to derive the…

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 64 dx

A: The given integral is ∫x2-64x3dx. Let us assume u=x2-64 and v'=1x3. Differentiate u with respect to…

Q: Evaluate the integral. (Use C for the constant of integration.) -2t te dt

A: Let the given function is:

Q: Use integration by parts to evaluate the definite integral. | t² In(t)dt Give an exact answer

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Q: Evaluate using integration by parts. .5 x° In (x)dx x° In (x)dx=| (Type an exact answer.)

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Q: Use a summation to find the integral from 0 to 4 of f(x) 2x + 1.  Then check it using the power rule…

A: Integration and derivative

Q: p) By using integration parts, show that i. S(In x)²dx = x(In x)² – 2x In x + 2x + C.

A: As per guidelines we have to solve one question Please repost other questions again

Q: 4 -dx is divergent. 1-2х (b) Show that the improper integral

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Q: 2 =dx converge or diverge. - 4 2. (a) Determine whether the improper integral| 2 XVx (b) Hence…

A: Given: ∫2∞2xx2-4dxTo determine whther this integral is converges or diverges

Q: the double integral dg dx Evaluate

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Q: y=-3 x=- V25 – x – y dxdy=

A: To solve the following double integral

Q: Use the specifie substitution to find or evaluate the Integral. (Use C for the constant of…

A: To solve the integration uisng substitution method

Q: Using transform, x = V5rcos(0), y = 2rsin(0) find the product of the integral dxdy

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Q: (a) Explain why | dr is divergent. (b) Find all value(s) of t > 0 for which the integral / 1 dx is…

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Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

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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.