2 = dx /-x² + 4x

Q: Find or evaluate the integral by completing the square.

A: Consider the polynomial: ax2+bx+c. We try to obtain an expression of the form, kx+d2+e from the…

Q: Evaluate the integral of dx / (x + 2) from -6 to -10.

A: The complex form of integration can be converted to simple integration form by  using the…

Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

A:

Q: Evaluate the integral by completing the square: dx 4x2 + 4x + 10

A:

Q: Evaluate the integral: V1 + 100x?dx

A: to solve the integral we use method of substitution

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ x dx/x2 - 3x + 2

A:

Q: Evaluate the integral by first completing the square.

A:

Q: Evaluate the integral by completing the square: dx 4x + 4x +5

A: Solution: The objective is to find the given integral

Q: Evaluate the integral of dx / (x + 2) from -6 to -10

A:

Q: evaluate the integral.

A:

Q: Use the Table of Integrals to evaluate the integral.

A:

Q: Find the Integral by using the substitution method.  x(7-x^2)^1/2

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

Q: Evaluate the integral. S (4x' – - 3x? + 2x) dx

A: The integration of the term 4x3-3x2+2x limit from 1 to 2.

Q: Find or evaluate the integral by completing the square. dx x* + 12x² + 37

A:

Q: Find or evaluate the integral by completing the square

A: Firstly, we make coefficient of x^2= -1, then we add or subtract the  square of ( coefficient of…

Q: Find or evaluate the integral by completing the square.

A: Find or evaluate the integral by completing the square.

Q: evaluate the integral from 0 to sqrt(2) x2/(4-x2)3/2 dx

A:

Q: Find or evaluate the integral by completing the square.

A: Our Aim is to evaluate the integral given below :-∫1-x2-4xdx -(i)

Q: evaluate the integral.

A:

Q: 19. (+ 2x 4) dx

A: ∫ af(x)±bg(x) dx = a∫f(x) dx ± b∫g(x) dx . ∫xn dx = xn+1n+1+C

Q: Find or evaluate the integral by completing the square

A: Consider the following integral:…

Q: Evaluate the integral. 14) x6(x7 - 6)4 dx

A:

Q: Evaluate the integral: |(322 + 1)(x³ + x+2)*dx

A:

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.)

A: Let's look at the denominator.The denominator = 9x2 – 18x + 36 = 9x2 – 18x + 9 + 27 = (9x2 – 18x +…

Q: Find or evaluate the integral by completing the square.

A: Given: ∫-23dxx2+4x+8

Q: 3x 2 dx

A:

Q: Evaluate the integral x Cx²-3) dx

A:

Q: .3 2х — 3 -dx 4 x –x

A: First break the given Integral  Then take 4x- x^2 = u and in other one complete the square  Finally…

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

A: Given: The integral,∫dx5x2-10x+20.

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integratic 1 dx…

A:

Q: dx 5x2 + 16

A:

Q: -10x5* dx -

A:

Q: Evaluate the integral. 0. (4.4x2 - 1) dx

A:

Q: Find the integral of So 7x+2x² (x-4)(2x+3X2x+1) dx

A:

Q: dx x2 – 2x + 50

A:

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) x²…

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

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ x dx/x2 + 4x + 3

A:

Q: Evaluate the integral of (x^2)/(x^2 + a^2)^3/2 dx

A:

Q: Evaluate the integral of x2 sqrt (x2+7)dx

A:

Q: Find the integral 2x /4-x4 dx

A: The given integral is ∫2x4-x4dx

Q: Evaluate the integral: | x(4 - x)3/2 dx'

A:

Q: Compute the integral by algebraic substitution:  ∫3x^5√16-x^2 dx

A: The given integral is: ∫3x516-x2 dxLet, I=∫3x516-x2 dx⇒I=3∫x516-x2 dx    -1

Q: Evaluate the integrals

A: Given: ∫24xπ-1dx

Q: Find or evaluate the integral by completing the square

A:

Q: Solve the function 3x4ex^5 dx on the integral from 2 to 3

A: Given:

Q: Evaluate the integral.

A: Integral:∫2xxdxLet, x=z      12x dx=dz

Q: evaluate the integral.

A:

Q: Evaluate the integrals.

A: To evaluate : The integral ∫052x-8dx.

Q: Evaluate the integral. In(9 x – 8) dx -

A:

Q: Evaluate the integral |- 5x + x3 - 2 x5 dx 3

A: Topic:- integration

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.