calculate the Integral by taking NX=ny=4 with simpson's rule. there is a tip given 1-[(x +1)dx integralini Simpson kuralı ile, n,=n,=4 alarak hesaplayınız. b-a h 3D Ipucu: [f(x)dx="(vo+4y +2v2 +4y3 +2y4 +...+2yn-2 +4yn-1+ Yn). 72

Q: Consider the subspaces of R5 U = span {⃗u1 = (1, 3, −2, 2, 3), ⃗u2 = (1, 4, −3, 4, 2), ⃗u3 = (2, 3,…

A:

Q: Evaluate he integral isin (x+rJl dx

A: given integral, I=∫03π/2sin(x+π) dx we have to evaluate given integral

Q: cosh / 2x 18) dx Vx² sinh³ /2x

A: The given integral: This can be rewritten as, To evaluate the integral: Apply linearity the above…

Q: (Sy?-8X46) dx =?

A: We need to evaluate ∫045x2-8x+6dx

Q: 1 dɔ V9-x² 3

A:

Q: (1–z²)³/2 Evaluate f dæ VI 2 - arcsina – zVI-z² +C Answer: |

A:

Q: Q2:A/ Evaluate the integrals 1 sec²(eVx + 1) dx J Vxe-V

A: Given: ∫1xe-xsec2ex+1dx Consider, u=ex+1, du=ddxex+1=ex+1ddxx+1=ex+12xdx

Q: r430 sin x 160 cos2 x(16-sec² x)

A:

Q: 3. Evaluate the improper integral: dx | Tale + 1)'

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Q: 3 4 Sx-3 dx x2+8x+41 (x+2)2 x2+9

A: Given,          ∫2x-3+3x+22+4x2+9+5x2+8x+41dx

Q: 5 3) S-²³2 235-1 dx a) Briefly explain why this integral is improper.

A: Follow the procedure given below.

Q: et dx 9 + e" Evaluate the integral using the substitution u = 9+ e". et dx 9 + e* +C

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Q: Q3) Use substitution to find the following integrals a. f sec²x √tan x dx b. dx x3 Sa (1+x4)5 C. csc…

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Q: Use Trapezoidal and Simpsons 1/3 rule to estimate integral ( - 2x° + 7x - 5) de.

A: The expression ∫13x3-2x2+7x-5dx. We have to use Trapezoidal and Simpsons 13 rule to estimate the…

Q: Use U-substitution to find the integral: 2 1 dx

A: Given,          ∫1x22-1xdx

Q: How does mathematics help to organize pattern and regularities in the world?

A: Mathematics is in everything in the world. Patterns in nature can be visible in flowers, waves,…

Q: Evaluate |- 1 =dx. a) xVx* +1

A: Given: ∫1xx4+1dx

Q: 1 nº 1 (2n-1) ( 2n + 1) 9. b. d. I

A: First we will do the partial fraction and find the nth term of the series as fractions then we will…

Q: Evaluate the integral į (1 – x– 4x° + 2x*)cx using multiple-application trapezoidal rule with n = 2

A: Given, fx=1-x-4x3+2x5 The trapezoidal rule to approximate the area:  ∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+.…

Q: Use the Midpoint Rule to evaluate the integral Sx-dx.

A: Midpoint rule:Let f(x) is a polynomial of degree ⩽n-1Let the midpoint x1=a+b2 and…

Q: 18. Sx²Vx3 – 4 dx a) Let u =x^3-4 b) Find du c) Find dx d) Evaluate the integral…

A: a) Let u=x3-4So, du=3x2dxor, dx=du3x2

Q: trapezoidal and Simpson's rules.

A: Solve the given integral ∫02∫01ex+ydxdy by trapezoidal and Simpson's rule.

Q: Use geometry and properties of integrals to evaluate

A: we have to  integrate the given integral ∫01(2x+1-x2+1)dx

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.