13. Find the integral using the u substitution method Jx(x+1)*dx

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: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

Q: S,(4y³ +-) dy y3.

A:

Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: 14 Find the integrals using integration by parts. a. fx(x + 4) dx c. fx'e"dx e flnx'dx d. [(In x)°…

A: (g) The given integral is, I=∫lnxxdx Rewrite as, I=∫xlnxdx Here, ∫udv=uv-∫vduu=lnx and du=1xdxdv=xdx…

Q: Find the general integral and compute 3 diferent solutions for : xzx+(x+z)zy=y-x

A:

Q: 3. Evaluate the integral Sx cosx dx.

A: Please see the below picture for detailed solution.

Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

A:

Q: Evaluate the integral. 9. dx J2 (x² - 1 1)3/2 Additional Materials Type here to search

A:

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

A:

Q: 2.) Evaluate the def inite integral dx o x²+4

A:

Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Q5. Evaluate the improper integral dx x(Inx)7

A:

Q: Find the integral. J 3 x√9 - (In x)² + C dx

A:

Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

A:

Q: 3 by taking n= 6 [In x · dx solution of the integral with Simpson's • method 3. (y, + y2 + y4 + y3 +…

A:

Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: 14. Find the equivalent integral of * S x(x+1) O-f3dx + f 3d x+1 dx OS÷-1# R x+1 01 Of //dx -…

A: Here we have to apply partial fraction.

Q: .3 Evaluate the integral LST wy+x*v+vz) dzdydx 0, 2.

A:

Q: aluate the Cauchy principal value of the given improper integral. dx (x² + 1)²(x² + 9)

A:

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: Evaluate the iterated integral. 4 1 (3x – 5y) dy dx -1

A: We need to evaluate the value of the following iterated integral ∫14∫-113x-5ydydx

Q: 3. Evaluate the integrals. dx ( Use u = Vx(1+x)

A:

Q: dx integralini hesaplayınız. x(In x)

A: Fundamental theorem allows us to compute definite integrals using the antiderivatives. It states…

Q: 5) Find the follow ng integrals dx 5 Sin'x cosx de JT-6x assecextany dx d)J2-x dx e) change limits…

A: Since you have posted multiple subparts question in this question so I have solved first three parts…

Q: 1. Use integration by parts to find the integral below. In(x19)– 9x10+C a. b. x ·In(x1)– 10x10+ C c.…

A:

Q: 15 Evaluate the improper integral J. (x- dx

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Evaluate the iterated integral of 2 2x . (x2 + 2y) dy dx

A: Evaluate the double integral

Q: 1. Compute the indefinite integrals: A. [4x+ Vx dx 3x+xdx В. B. S*dx

A: Question is solved.

Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: Evaluate the integral.

A: We have to evaluate the integral: ∫x3xx2+3y2dy Here we have to integrate with respect to y so x2…

Q: 1. Evaluate the integral using Integration by Parts. (a). S In(Inx) dx.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: (3) Evaluate the iterated integral , " (3 + x² +v²) dx dy.

A: First integrating with respect to x and then with y

Q: 4. Determine the following integrals 4.2 - dx - a x

A:

Q: 1 uate the improper integral dx. x(In x)3

A:

Q: Evaluate the integral (i) S 3x3 sin 4x dx (ii) S In (x³ + x) dx

A: This section looks at Integration by Parts (Calculus). From the product rule, we can obtain the…

Q: Evaluate the Cauchy principal value of the given improper integral. 1 [ (x² + 4)² dx

A:

Q: Compute the given improper integral. Enter the exact value of the answ 13 1 dx x² – 25

A: Here we have to find the exact value of ∫5131x2-25dx=?

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: 1) Evaluate. Јx cosh ax dx 2) Evaluate the integral. (In x)² dx x3 1

A:

Q: II. Evaluate the following integrals: x- 2 1. J- -dx +1 2. J; -dx 8х + 3 3. J- x -4x-9

A:

Q: 2. a) Evalute the following improper integrals dx Vx – 3

A: We will solve the problem.

Q: Q2: Evaluate the integral fx In x dx using by parts formula

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

A:

Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

Q: a) Compute these two integrals shown below using one application of trapezoidal rule and Simpson's…

A: Given that ∫23x dx ∫-66x2cosx dx we have to calculate given integral using  trapezoidal rule.

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.