Evaluate the integral using the method of partial 2x3 –21x²+32x+22 x² –10x+21 fractions: dx

Q: 9ェ3- 3エ+1 13- 12

A: Given integration is                                                ∫9x3-3x+1x3-x2dx we will convert…

Q: 4x3 + 4x? – 2x + 4 dx - (x² + 1)?

A:

Q: x² + x – 2 (3x – 1)(x² + 1)

A:

Q: Use the three-segment trapezoidal rule to estimate the integral of f(x) = 0.2 + 25x - 200x2 +…

A: a=0 and b=0.8 given put x=0 in equation f(0)=0.2again put…

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ dx/(x2 - 1)2

A: Using partial sum we get:

Q: Evaluate the integral of 3dx/(2x^2 + 4) from 0 to 0.2 *

A:

Q: Evaluate the integral using the method of partial 2x3–15x²+17x+13 x2–7x+12 fractions: dx

A: NOTE: Refresh your page if you can't see any equations. . take long division…

Q: (6x²+ 40x-20)dx 1. S. (x-3)(9x²-4)

A:

Q: 9. dx. x² + x – 20

A: The explanation of answer as follows

Q: Use partial fractions to evaluate the integral 81/(( x^2)(x−9)) dx.

A: Explained below

Q: form long division on the integrand, write the proper fraction as a sum of partial fractions, and…

A:

Q: Evaluate the integral. .V3/2 35x2 dx V1- x2

A:

Q: Evaluate the integral. V2/2 5x2 dx V1- x²

A: We will solve the problem.

Q: Determine the integral: x²cosxdx (A) x²sinx+2xcosx-2sinx + C (B) x²sinx-2xcosx+2sinx + C…

A: topic- indefinite integral

Q: Evaluate the following integral using partial fraction x* – 2x2 + 4x + 1 х3 — х2 — х + 1 -

A: We will find the integral using partial fraction  as following.

Q: Evaluate the integral by algebraio substitution then partial fractions: * 1 dw. w + 2/1 – w +2

A:

Q: Evaluate the integral by partial fractions decompositior Зx3 + 1 dx x3 – x² + x – 1

A: Here we have to evaluate,

Q: Evaluate the integral using partial fractions: ∫ x+4 / x2+2x+5 dx

A: Here we use partial fraction and integration of the particular function : ∫dxx2+a2=1atan-1xa+C

Q: Evaluate the integral. dx :- X>8 x2Vx² -64 S- xp x²Vx² - 64 %3D

A:

Q: Evaluate the integral by Partial Fractions ∫6x^2-3x/(x-2)(x+4) dx

A:

Q: Use partial fractions to find the exact value of the following integral 31² +3 23 + 3x

A: First do partial fraction then do integration

Q: Determine the integral: x²cosxdx A x²sinx+2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C Cx²sinx +…

A:

Q: Solve the integral using partial fraction decomposition method, four digits after comma: 5x2 - 8x +…

A: We will solve the following

Q: Evaluate the integral 1 / / emax{x²,v²} dydx

A: integral of  ∫01∫01emax {x2,y2}dydx

Q: Evaluate the integral using partial fraction decomposition

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integrals. x+9 S: -dx 2x³ - 8x

A: To express the integrand as a sum of partial fractions and to evaluate the integrals.∫x+92x3-8x dx

Q: Use Method of partial fractions to evaluate the integral : S 2x+7 dx x2-9x+14

A:

Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C C…

A: integration

Q: 9 dx. +x – 20 х2

A:

Q: За — 1 (x – 2)(x + 5)

A:

Q: Evaluate the integral by Partial Fractions 6x? – 3x dx. (x – 2) (x + 4)

A: To integrate ∫6x2-3x(x-2)(x+4)dx, take the partial fraction of ∫6x2-3x(x-2)(x+4)dx and obtain…

Q: 4x4 +1 dx 2г3 + х? —

A: We are given the Integral:∫4x4+12x3+x2-xNow , using long Division…

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 using partial fraction decompoșition (х — 1) J (x2 – 4x – 5) -

A: Given the integrationI=∫(x−1)(x2−4x−5)dx

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ x3 dx/x2 - 2x + 1

A: Given: I=∫x3dxx2-2x+1 for evaluating given integral, we simplify given expression as below…

Q: Evaluate the integrals using the substitution method of 3x2(x3-4)9 dx

A: Given: Let I=∫3x2x3-49 dx To Find: To evaluate the given integration using the substitution method.

Q: Evaluate the integral. (Use C for the constant of integration.) 6x2 + 7x + 6 xp (x2 + 1)2

A:

Q: Evaluate the integral by first performing long division on the integrand and then writing the proper…

A: Given problem:- Evaluate the integral by first performing long division on the integrand and then…

Q: Evaluate the integral using partial fractions: ∫ 10 / (x-1)(x2+9) dx

A: Solution:To evaluate the integralLet I=∫10x-1x2+9dxFormula:∫f'(x)f(x)dx=ln f(x)+C

Q: Evaluate the integral f(4x³ + 5x* + 2)dx

A: ∫xn dx xn+1n+1+C ∫a dx ax + C

Q: Calculate the integral. 2x° (x + 2)²dæ

A:

Q: Evaluate the integral by first performing long division on the integrand and then writing the proper…

A: Consider the following integral: ∫3x4+15x2+5x3+5xdx=∫3xx3+5xx3+5x+5xx2+5dx=∫3x+5xx2+5dx Consider the…

Q: dy J y3-2y2 у3-2у?

A:

Q: Use the method of partial fractions to evaluate each of the following integral. Show your work!

A: To find the integration by using partial fractions

Q: 9 Express the in tegrand ar a sum of parhal fraction and evaluate tte ntegral. %3D XXXH)

A: ∫2dxx(x+1)

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 using substitution as an aid: x (2x* + 1)2dx

A: Consider the integral

Q: 6x2 – 3x dr. J (x – 2) (x + 4)

A: Since the degree of the numerator is equal to the degree of the denominator, we need to first…

Q: Evaluate the integral from 1 to 2 using partial fractions: ∫ (4x2-7x-12) / x(x+2)(x-3) dx

A: To evaluate the integral: ∫4x2-7x-12xx+2x-3dx Solution: Decomposing the integrand using partial…

Q: 1 dx x2 + 3x

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.