Trapezium Rule y, Area = [ydr - [y, +2(x; +y; ++Y-)+3,] where h= b-a b Discuss how dx affects the accuracy area.

Q: 1 1. J dx x2 V9x²-81

A: Wr have to evaluate the integral.

Q: (f) / sec“ y dy. tan5

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Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: (ど4ー) 2dx 4 X(3(Inx)*+121nx-15)2 2)

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Q: Given the edge of a square is about 100 cm, by how to measure it such that the

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Q: sec? (1/x) dx. 9: (16pts) Evaluate

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Q: fostp Ex=(Xzy)=-3:52-25)

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Q: 2. dx 2. Solue integra

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Q: solve 2 (pedoe tydy +2d₂) ² 2 = {(2²-x²=y²2) (seds tydy + z dz/d2} z

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Q: JA 1 dx. /4-

A: ∫14-x2dxFormula∫11-x2dx=sin-1(x)+C

Q: Differentiate  (sin 2t)/t.

A: ft=sin2tt

Q: Point M(-6,8) is dilated from the origin with a scale factor of 1/2. What is the coordinate of M'?

A: The idea of dilation is to make something bigger or smaller ( according to scale factor). Here the…

Q: Lion 1-y If x = Show that 1+y dy V1-y

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Q: y-Castesinz şinz

A: The detailed solution is as follows below:

Q: integrate dx / x^3-x^2  (I do not understand how to set up and complete the A+B+C part

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Q: f (x) = esin(x²), [0,3]

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Q: Evaluate. (use C for aonstant of intgration) dx 2 X "- 3

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Q: d(arctanx+sqr root x))/dx

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Q: Consider R4 with coordinates t, x, y, z. Let a = xdt / dx + xdy dz. Calculate a ^ a.

A: Given: is with coordintes .Let .To Find:The value of .Concept Used:

Q: Differentiate, hcx) = In (x-Vr

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Q: Secx tant I seex+ Secx+3

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Q: alla la ecuacion ordinaria de cada elipse B)    A(0,4);B(0,-4),LR=20/3

A: Consider the given vertex 0,b=0,4 b=4 Latus rectum L=203

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.