2x Evaluate the improper integral J dx, if it exists. (x2 + 64)2

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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Q: Q#01: Find the complete integral of x²p? + y²q? – 4 = 0 using Charpit's method.

A: To find the complete integral of using Charpit's method.

Q: The improper integral 1 dx is 'o 2V1-x²

A: this can solve simply by apply the integration formula

Q: dx 6. Evaluate the improper integral. x² +3x+ 2

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Q: 5. Evaluate the definite integral (1+Inx) а. b. S dx. 2x+3

A: a) ∫1e1+ln x2xdxb) ∫-1112x+3dx

Q: Find the complete, singular and general integrals of p3 + q3 = 27z. %3D

A: We have to find the complete, singular, and general integrals of:  p3+q3=27z

Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

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Q: dx Evaluate the improper integral x(lnin x )²

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Q: 2x Evaluate the improper integral dæ, if it exists. (x2 + 64)2

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Q: Find the complete integral of the z'(p°z² +q°)=1

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Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: 1. ſ (x-1)dx x2+5x+6

A: The given integration is ∫(x-1)x2+5x+6 dx  We have to find the integration for the given integral

Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: 2x Evaluate the improper integral J dx, if it exists. (12 + 81)2 -00

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Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

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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: The improper integral 2dx 0. 1-x2 3 T

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Q: 1 4. f₁² (1-x²) dx 5 2

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Q: Q.5 Evaluate the integral with the aid of the formulas 5,6, and 7. dt 9-4t2

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Q: Evaluate the integral f 2x (x² + 2)° dx using the substitution u = x? + 2. | 20(a* + 2)" de +C

A: The given integral is: I=∫2xx2+26 dx

Q: Evaluate the improper integral 1). Sa -2* 2 dx x2-2x

A: Given: ∫3∞2x2-2xdx We have to evaluate the improper integral.

Q: 3z+4 dr Use the appropriate substitution to evaluate the following integrals: e %3D O e3a+4 + C ©…

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Q: Solve the double integral J, J, (1+ xy)² dydx In n(금) O 2ln(5) – In(3) O In(3) – 4ln(5)

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Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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Q: 4. S dy y³-2y²

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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: dx Evaluate the improper integral if it exists 3 .1 O 8.2 0 The improper integral diverges 3 O 6.4 O

A: Option (4) is correct. Answer is 6.

Q: Q.5 Evaluate the integral with the aid of the formulas 5,6, and 7. dt V9-4t2

A: We have to solve integration .

Q: 5x Q5 integral Evaluate the in dx (x²+1)(2.x-2)

A: Let I=⇃5xx2+12x-2.dx    I=⇃52xx2+1x-1.dxBy Method of partial fractions…

Q: 5x dx. - 6 Compute the integral x2

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Q: Q2/Evaluated the integrals v2 1- f– (1-v2 )2

A: The integration of v2/(1-v2)5/2.

Q: 2. Evaluate these indefinite integrals: dt (d) S; dt 2t2+5t+3

A: Given that a integration  and we solve it by using general property of integration. Here i attached…

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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Q: The value of the improper integral / 36 z² e ² dz = 12e1 O - 36e 1 O 36e 1 O 12e 1

A: We need to evaluate the value of the following integral I = ∫1∞36x2e-x3dx

Q: 3 3y Evaluate the iterated integral ry de dy.

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Q: Evaluate the improper integral t* e-2t 3+e-4t at

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Q: dy J. 1. 2.

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Q: 2 Evalu ate the fllowing integral - R Is the regiovi be undéd by the grapis x:2, y= x-5, and…

A: We will evaluate the required value.

Q: Evaluate the integral. 2 (8t i - j+ 3t5 k) dt

A: We first separate the integral

Q: 9. In evaluating the improper integral dx , which of the following is true? (1– 3x)2 3 (A lim 3x 1…

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Q: Q.1 Evaluate the given integrals using part I of the Fundamental Theorem of Calculus. [3 Marks] i.…

A: You need to find the integral of the given functions using the fundamental theorem of integration.

Q: 1 (x² +a) b dx is In 5x The resulting integral of +eTan-1 + C, where a, b, d, and e are integers. x³…

A: Given:∫5xx3+x2+4x+4dx= ln⁡x2+a1bx+d+eTan−1⁡x2+C Let, I=∫5xx3+x2+4x+4dx ⇒I=∫5xx2(x+1)+4(x+1)dx…

Q: 1. Evaluate the integral Vi-x² ex?+y*dydx.

A: 1. The given integral is, ∫01∫01-x2ex2+y2dydx. Convert the integral into polar coordinates as…

Q: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: Evaluate the iterated integral: - 7 -X = S S e-* dydx е 8

A:

Q: dx Evaluate the improper integral (x-3)2

A: Given query is to find the value of the 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.