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Q: Evaluate the indefinite integral; f Vtan 3x sec2 3x dx OA)-(2(tan [3x)^(3/2) ] /9 + C OB) I DON'T…

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Q: / 1 – x2 dx (c)

A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

Q: The value of the integral Vx dx computed using Trapezoidal rule with 2 subintervals is (Rounded upto…

A: The trapezoidal rule uses the area of the trapezoids to approximate an integral. Using the…

Q: Evaluate the integrals using integration by parts. ∫x sec2 x dx

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Q: com Ise Find the indefinite integral using integration by pa x cos 9x dx;u= x, dv = cos 9x dx egin!

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

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

Q: Evaluate the integrals ∫2 sec3 x dx

A: To Find: The following integral Formula Used: Common Integral :

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

A: Given

Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: calculate the integral.

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. X cos 6x…

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Q: Find the approximate value of integral from 0 to 10 1/√(x2+1)dx to 4 decimal places using Simpsons…

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Q: Find the complete integral of (1 az 1 dz z dx2 1 az Exe z dx3 z dx *Ex 7x Ix =|

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Q: Evaluate the integrals using integration by parts. ∫(x2 - 5x)ex dx

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Q: Approximate the integral from 2 to 14 (x2 -5)dx using 4 rectangles

A: To find the area under the curve using rectangles, the Reimann sum is used.First, we need to find…

Q: Evaluate a. Fв- x-3Dаx

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Q: 2 -y2 dydx e 0. 2x

A: The answer is given as follows:

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Compute this improper integral showing all steps.  integral of (x/(x^4)+9) dx from 0 to infinity.

A: please refer to the image below

Q: 1+cos 4x dx 1-cos 4x 10.

A: Evaluate integral

Q: Find the indefinit integral of (3-2x)2 dx

A: Given ∫3-2x2 dx

Q: Evaluate the integral * In 2 tanh 2x dx

A: We have to find Integral of given function.

Q: 4. f In (2x + 1) dx =

A:

Q: Find the integral. In 8x dx

A: I=∫ ln 8xx dxln 8x =t18x(8) dx = dtdxx =dt

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 6x…

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Q: Evaluate the integrals using integration by parts. ∫ ex cos 2x dx

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Q: Find the integral

A: To integrate ∫ln|4x+5|dx, use the substitution method and consider 4x+5 as t. Differentiate both…

Q: Evaluate the integrals using integration by parts. ∫e-2x sin 2x dx

A: the given integral is: ∫e-2xsin2x dx we have to evaluate the integral by using integration by parts.…

Q: Vsin x + 1 cos x dx

A:

Q: Pls kindly help evaluating integrals by first differentiating Theorem Intergal(0,infinite)…

A: I am going to evaluate the given problem using the first differentiating theorem which also the…

Q: find the indefinate integral of sin^5(x)cos(x) dx

A: I = ∫ Sin5x  Cos x dxLet Sin x = tCos x dx = dt

Q: Evaluate the integral using integration by parts where possible. x In(8x)dx

A: Given: ∫12 x ln(8x) dx To find: Value of the integral.

Q: Evaluate the integral using Integration by Parts. 2z2 cos 5z dz

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Q: Compute the indefinate integral. integral (1-sin^2(x))/cosx * dx

A: Consider the given integral.

Q: 2. Calculate the indefinite integrals for the following functions as integrands: 1 x In ¤/(In x)2–1…

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Q: Evaluate the integrals ∫cos x cos 7x dx

A: To integrate: ∫cosxcos7xdx.  We know that cosacosb=12sina+b-sina-b. Therefore, using the above…

Q: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

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Q: Find the integrals using integration by parts. b. [ Vx In /xdx

A: Consider the given: ∫xlnxdxIntegration by parts:∫udv=uv−∫vdu

Q: Evaluate the integrals using integration by parts. ∫ x2 sin (1 - x) dx

A:

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: Evaluate the integrals using integration by parts. ∫ cos-1 (x/2) dx

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Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

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Q: compute the integral of    "(sinx * tanhx ) / ln(x+0.01)" from 1 to 5 to at least 6 significant…

A: Given :  ∫15sinxtanhxlog(x+0.01)dx

Q: 2. Estimate the integral using Simpson's approximation rule with n=4: sin t dt

A: To estimate:∫0πsint dtn=4

Q: In 2 tanh 2x dx

A:

Q: 8. 3 dx 8- x X

A: Formula

Q: Evaluate the integral S(VE + vaj*dx; ais constant

A: Explanation of the answer is as follows

Q: find | (In(x)dx 2 3 Improper Integral

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Q: Evaluate the integrals ∫8 sin4 y cos2 y dy

A: the given integral is: ∫8 sin4y cos2y dy we have to evaluate the given integral.   let the given…

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.