By using integration by parts, the value of the integral In 2x dx is попe x In 2x – x+c 1 x + c 2 Ox In 2x x In 2x + x +c

Q: The area bounded by y=3Vx and 2y =3x is revolved about the x-axis. Using cylindrical shell method,…

A: Consider

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 region of integration in the integral 2x So So a f (x, y)dydx is rectangle Select one: True…

A: The region of Integration in the integration in the integral  ∫02 ∫02x F(x,y) dyd2  is a rectangle…

Q: Evaluate the integral using integration by parts 4X Xe dx 4x Xe dx =

A: The given integral is: ∫xe4xdx Here to use the integration by parts: ∫uv dx=u∫v dx-∫ddx(u)∫v dxdx To…

Q: The region is bounded by x+6=0 and y^2+x+2=0 is revolved about x=-6. find the integral in finding…

A: Consider the provided question, The volume for solid of revolution between the curves x+6=0 and…

Q: By using double integrals find the area between x = – y², lines y = x – 4, y = -2 and y = 2.

A:

Q: Use integration by parts to compute the integral S xsin(4x)dx and Inx dx

A:

Q: 4. Evaluate the integral using Trapezoidal and Simpson's rule with h = 0.5, 0.25 and 0.125. = 1+ 2x3…

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

Q: Evaluate the integral: Integral with bounds of 2 and -2 ez/2/ez/2+1 * dz

A:

Q: π Find the area of the region enclosed by y = sin¯¹(x), y = and the y-axis without using integration…

A:

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -6t sec2…

A: Given integral is : ∫-6tsec2tdt=-6∫tsec2tdt

Q: evaluate using Integration by Parts.

A: Use the method for integration by parts. Assume the value for u and v’.

Q: 1-r x² + y² dydx

A: Area of a function fx, y for a≤y≤b is given by  ∫abfx, ydy So, ∫-1-x21-x2x2+y2dy represents the area…

Q: Evaluate the integral using integration by parts. 3x cos (5x) dx Se 3х cos (5x) dx =

A: Let u=cos(5x) and dv=e^(3x)dxFind du and v from those.

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -9x In(2)…

A:

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

A:

Q: Use Integration by Parts to evaluate the integral. x In(x) dx 3 In(4) - 4 In(2) + 3 In(2) – 3 1…

A: Given:

Q: 3 4 Sx-3 dx x2+8x+41 (x+2)2 x2+9

A: Given,          ∫2x-3+3x+22+4x2+9+5x2+8x+41dx

Q: 2. Express the shaded area of the region shown below by double integrals of order of integration (1)…

A: Given figure :

Q: the region bouded by x=y+2 and x=y^2 revolved about x=-1. Find the integral in finding the volume of…

A: The volume of the solid generated by revolving about the y−axis a region between the curves x = f(y)…

Q: By using double integrals in cartesian coordinates, find the area in the first quadrant that bounded…

A:

Q: Using Integration by Parts, the integral [(x8. is equal to x10 5 - the above + 2x⁹) In x dx…

A: Given: I=∫x8+2x9lnxdx   Apply the integration by parts to solve the given integral. ∫udv=u·v-∫vdu

Q: By using double integrals, find the area of the regions enclosed by: (a) y=4-x² and y=3x (b) y=sinx…

A: Area of region between two curves.

Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of…

A: ∫(2-x)2x dxApply linearity:=-∫(x-2)*2x dxIntegrate by parts ∫fg'=fg-∫f'gf=x-2 and g'=2xf'=1 and…

Q: By using integration by parts, the value of the integral In 2x dx

A: The given integration is ∫ln 2x dx

Q: 1) Express , 4xyz dV , where E = [0,1] x [0,2] x [0,3] by using different orders of integration.…

A: In the given question we have to find the integration ∫∫∫E4xyzdVwhere E=[0,1]×[0,2]×[0,3]  is the…

Q: ii. y = 4 - x2, y = 3x

A: topic - double integration

Q: Using integration by parts, the integral | sec³dx is equal to

A: Here we use the integration by parts:

Q: 1) Express , 4xyz dV , where E = [0,1] x [0,2] x [0,3] by using different orders of integration.…

A:

Q: 3. V1-x². /1 — х2 хdx

A: To solve this integral, a substitution is made. The substitution taken is 1-x2=u. This equation is…

Q: Given that x2 dx use this fact and the properties of integrals to evaluate (2 - 3x2) dx. %3D

A: Answer is- 1 Explanation is given below...

Q: 2. Express the shaded area of the region shown below by double integrals of order of integration (1)…

A: find area using double integration

Q: Evaluate the triple integral. 4 v16-x' V16-x'- dy dz dx

A: Given integral is eb=valuated as follows.

Q: Match the integrals in the left column with the correct evaluation method in the right column. Using…

A: We have to match the left  column with the right column.

Q: Compute the double integral , (62xy – x²) dA over the region bounded below by y = x', above by y =…

A:

Q: Use the form of the definition of the integral given inTheorem 4 to evaluate the integral. integral…

A: To evaluate the integral: ∫022x-x3dx Evaluating the integral.…

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv: -9x In(x)…

A: By integration of parts: ∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx

Q: [xt xtan xdx

A:

Q: Reverse the order of integration in the iterated integral and then evaluate the integral. VE (2-x…

A: From the limits of integration, the region bounded by the curves y=0, y=2-x2, x=0, x=2. The region…

Q: Use integration by substitution and/or by parts to compute the integral Jx In (5 +x)dx .

A:

Q: Evaluate the integral using integration by parts with th xex dx; u = x, dv = e3x dx 3r 1 3x

A:

Q: 1 Oblicz d.x, Vax ах — х2 – x²

A: In this question, we have to evaluate the improper integral. Here we also use the property of Beta…

Q: Evaluate the integral using integration by parts. 4x dx Xe 4x dx = Xe

A:

Q: Use the form of the definition of the integral given inTheorem 4 to evaluate the integral. integral…

A: we have to evaluate the integral: ∫01x3-3x2dx using the definition of integral, ∫abf(x)dx=limn→∞∆x…

Q: 6. Evaluate the intergral | (2x + V4 – x²) dx by using the properties of integrals and your…

A: Given: ∫-22 (2x+4-x2 ) dx To find: Value of the integral.

Q: (12) Sz sec¹z dz.

A:

Q: By using integration by parts, the value of the integral In 2x dx is попе o x In 2r -x + x In 2r -…

A: Option C is correct

Q: Svaluate x dx from the definition of RS-integral.

A:

Q: Sketch the region of integration and evaluate the following integral, using the method of your…

A:

Q: Use a double integral to find the volume of the indicated nolid. 12 z- 12-X-y 11 10 4. 6. y 6 y-x

A:

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.