x* + 10x dx

Q: Evaluate 2x(x2 + 2)*dx

A: First I have used  a substitution and made integral easy and then solved it.This is the process.

Q: 5x + 6x dx. Find х - 1

A:

Q: (x-1) 12-3x dx

A: It can be solved directly

Q: x² – 2x dx

A: Given integral can be written as By using the following substitution we get

Q: 4x-1| dx

A:

Q: 2x – x + 4 dx x3 + 4x

A:

Q: (x2-4x+8) dx

A:

Q: Find ∫ x2 e-x dx

A: Given : ∫ x2 e-x dx

Q: Find ∫2x dx

A:

Q: 4x + 2 dx +x+ 5 x2

A: We have to find solutions

Q: x + 3 -dx х — 1

A:

Q: Find dx Nx+7+X

A:

Q: -2x 4x -dx

A: We need to evaluate ∫0∞e-2x-e-4xxdx First we simplify the expression…

Q: x+ 3 dx Vx² + 6x

A: Given that a integration and we find its value by using general formulas of integral. We know that…

Q: ∫(x^3-4x)dx

A: The given integral is- I=∫x3-4xdx Then, ∫x3dx=x3+13+1=x44 & ∫4xdx=4x1+11+1=4x22

Q: Evaluate dx 2 1-x

A: We have to evaluate ∫23x1-xdx. We know that ∫dxx2-a2 = 12aln x-ax+a+C

Q: Find d^2/dx^2 x=1 (exlnx)=

A:

Q: x²(x³ - 2) dx

A:

Q: 5x*dx V1 – x³ .5

A:

Q: Evaluate x²|1 – 2x| dx.

A: We have to evaluate ∫01x2 1-2x dx.

Q: 2x + 2 dx x2 +1

A:

Q: S(3x* – 5xP +x=³)dx.

A: Given query is to find the integral.

Q: fx(x-1)³ dx

A:

Q: x5 - 5x (xª – 1) dx

A:

Q: | (7x)-1 dx

A: Integration is solved step wise .

Q: /1+ x²x5 dx

A:

Q: x evx²-1 dx Vx2-1 .2

A: We have to evaluate  ∫x ex2-1x2-1dx.

Q: (3-2x) dx

A:

Q: Evaluate ∫(x + sec2(πx))dx

A: The integral given is , ∫x+sec2πx dx Expand the integral ,  ∫x+sec2πx dx=∫x dx+∫sec2πx dx Solving…

Q: 6x dx 1

A:

Q: Find ∫(x2 + 1)2(2x) dx.

A: Let the given integral be y - y = ∫x2+122xdx                    ....................(1)y =…

Q: (4x+2x- 1)dx" 0

A: ∫034x2+2x-1dx lim ∑i=1nfxi∆x for each n we have ∆x=b-an=3-0n=3n

Q: Find (9x + 2)*dx. (9x + 2) dx =

A: To evaluate thee integral: ∫(9x+2)2dx For the first simplify the whole square and then take the…

Q: Find ∫sec3 x dx.

A: We have to find the integration: ∫sec3 x dx Assuming, I=∫sec3 x dx Rewriting the above integral,…

Q: sv x² + 2x dx

A:

Q: Find ∫ √(3 − 5x) /2x   dx.

A: Consider the given integral, ∫3-5x2xdx substitute 3-5x=u ⇒ dx=-23-5x5 ∫3-5x2xdx=2∫u2u2-3du now,…

Q: | (4x - 1)2_x dx

A:

Q: Find if x* -3ху +3у %37. dx

A: Given: x3-3xy+3y2=7 To find: dydx

Q: 5x - 9x +6 dx x - 2x +x

A: Solution of the problem as follows

Q: 1. S(2x° - 5x + 2)dx

A: We have to find the given integral

Q: xlnx-x dx. (Inx)3

A: We have to find the integral

Q:

A: Given,              ∫xx2+4x+5dx=

Q: Find ∫ (x + 2) / √(4 − x2) dx.

A: C=integrating constant

Q: 1. 4x°dx (2-x*) ° 6

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 4x √x +9 dx

A: Given integral ∫4xx2+9dx. The objective is to evaluate the integral.

Q: x² + 2x dx

A:

Q: Evaluate : |xtan-1x dx

A: The given integral is                                      ∫x tan-1x dx

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.