The integral x²/4 - x²dx can be determined using the substitution 4- x2 = t.

Q: Compute the integral ∫xdx/1+x4.

A: Let,

Q: Evaluate the integral ∫x2dx / (x−1)(x−2)(x−3).

A: We will use the partial decomposition

Q: Evaluate the ff. integrals using substitution: dx 1. S (5-2x)2

A: 1. Using substitution u=5-2x

Q: Calculate the definite integral of x^2 + 4x approaches from 1 to 3.

A:

Q: Evaluate the integral. xV1- x2 dx 14

A:

Q: x-3(x-1 + x)²dx

A: Given, ∫x-3x-1+x2dx It is required to evaluate the integral.

Q: Evaluate the integral ∫√x2−25dx.

A:

Q: Evaluate the integral [V9+x²dx

A:

Q: 6dx x - √ S 3√x²

A:

Q: Evaluate the integral: */64 – a°dz .3 2 -

A:

Q: Use the Simpson's Rule to evaluate the integral fx|x²dx 1

A: Given integral is ∫−11xx2dx. We have to evaluate the given integral by using Simpson rule. Here,…

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: x²dx V9-x2

A:

Q: Evaluate the integral dydx 3. 1-X 2

A: Use polar coordinates for simplification of the given integral.

Q: find a complete integral of q=3p2

A: Given that : q=3p2 It can be written of the form ,3p2-q=0                              ⋯1 Since 1 is…

Q: Approximate the integral of: f(x) = Vsin(x) + x* + 5 from x = -10 to x = -14 using N = 4 steps. (a)…

A: Given : f(x)=sin(x)+x4+5 a) using left hand sided rectangles We know that  ∫abf(x)dx=…

Q: 2.x D' -8 .

A:

Q: Evaluate the integral S (2x − 8)dx - x² - 6x + 18

A: Solution is below

Q: x2-6x+13

A:

Q: Evaluate the integral V212 -7x2 dx 1 – x²

A:

Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Evaluate the integral. 1 ds V5s - 9

A: Given,         ∫15s-9ds

Q: Evaluate the integral ∫xdx / √1+x2.

A:

Q: Given the integral of- 2x with respect to x. x2+x-12

A: Please refer to the image below.

Q: 1. S V16 – 4x²dx

A:

Q: Evaluate the integral 3 -x a. So Sox² exy dydx 0

A:

Q: x²dx 8. S a4-x4

A:

Q: x² XP aX

A: This is solve by substitution method

Q: 2 x'-2x+1 xp: 4x3

A:

Q: 1. Use the Table of Integrals in the back of your textbook to evaluate ∫11dx/x^2√16x^2+36 a.Perform…

A:

Q: The integral of x²Inx with respect to x is; A -(3lnx+1) +C ® (3lnx – 1) +C © 3lnx – 1) +C 3 D -(Inx…

A: Product rule of integration : ∫u.v dx = u∫v dx -∫dudx∫vdxdx dlnxdx = 1x ∫xn dx = xn+1n+1 +C In…

Q: Evaluate the integral from 0 to infinity of 1/[x2+5x+4] or show that it diverges

A:

Q: Evaluate the integral. 8 V1-t2

A: We have to evaluate the integral: ∫02281-t2dt We know the formula of integral, ∫1a2-x2dx=sin-1xa+c…

Q: Evaluate the indefinite integral. 7dx a In(3x) +C

A: We hae to evaluate  the indefinite  integral.

Q: Evaluate the integral sec^2xdx/√(1-4tan^2(x)).

A: Given :           ∫sec2x1 - 4tan2xdx   To evaluate the integral.

Q: Evaluate the integral of x(x-5)12dx  with limits from 5 to 6.

A:

Q: Evaluate the integral of cos^2 ydy

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Evaluate the integral -4x 1 - x2 1-x2

A: to solve the given indefinite integral put,

Q: Evaluate the integral S6x/( x²+1)(2x-2).

A:

Q: Use the indicated entry in the Table of Integrals to evaluate the integral. 2 9V 4x2 – 3 dx; entry…

A: Solve, as follows: I=∫1294x2-3dx=18∫12x2-322dx

Q: 2. Use the Table of Integrals in the back of your textbook to evaluate ∫11dx/x^2√16x^2+36 a.Perform…

A: While solving this indefinite integral, we need substitutions twice.

Q: Evaluate the integral.

A: Here given integration can be written as…

Q: Solve the integral equaher by eliminating the Inkegral = -3+) (3t -3ty(t) dt. = -3 for when ansusemg…

A: Differentiating both sides of equations. Differentiating integral using leibniz's rule.

Q: Evaluate the integral. 8*V1-x² dx x³V

A: Let, z=1-x2dz=-2xdxdx=dz-2x When x=0, then z=1 When x=1, then z=0

Q: Evaluate the integral. to dt 5/2 x2 (x² – 16}"-

A: Given:  ∫ x2 dxx2 -1652 =?Using Substittution Method:…

Q: the integral of dzwhere e is and 9-x S

A: by using Residue theorem we can solve the given complex integral

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.