Find the indefinite integral: 2- 2x + x2

Q: (27 dy 7. ソー

A: Definite integration

Q: xyzdV where E is the solid: 0 < z < 8 ,0< y< z ,0<x < y.

A:

Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

A:

Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

A:

Q: Evaluate the integral ∫dx/1+2x2.

A: Given :

Q: dy 6. So 1+y+1 6.56

A:

Q: Q3/ Evaluate the following integral and simplify it into the final form: x-6x-2x-3x+4 x'+2x+3

A:

Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

A:

Q: 2x 35. x2 + 6x + 13 -бх + 13

A:

Q: 9.* sec3 x tan³ x dx

A: The value of the given integral is (2√2 + 2)/15

Q: би + 12 du

A:

Q: – dx x Inx x²+1

A:

Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: 10 dR 25

A: Use basic integration  Here R varies from 25 to -10.

Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

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.