1 Use the Trapezium Rule, with seven ordinates, to evaluate In(sin.r+3)dxcorrect to four decimal places.

Q: Find 7'(t), given ř(t) = ( – 4cos( – 5t), 3 sin( – 5t), e*). - - F (t) =

A: Solve the following

Q: 4. The area which is inside the circle r = 8 cos e and outside the circle r = 2 cos 8.

A: Introduction: In polar coordinate, the equation of a circle centered at the origin with radius a…

Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: Show that 0, if m if m + n sin(nx) sin(mx) dx T, = n IT

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Q: Given the integral csc²u=cot²u+1 1+ cos2u 2 1-cos2u 2 sec²u=1+tan²u B cos²u=- sec (x-1) tan4…

A: According to our guidelines we can answer only one question or three subparts of a question. Other…

Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: 2, Sove the Following Riccati equâtion dy 2008?x- Sin?x +y? %3D 2 cosX

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Q: Estimate o cos(x2) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with n = 4.…

A: Given: ∫01cosx2dx To Estimate: The given integral usinga. Trapezoidal Ruleb. Midpoint Rule

Q: find the pauticuler soluhion fr + loy = x'_e*sin(8x)

A: Solve particular integral in above differential equations.

Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: Evaluate A = Se-* dx þy trapezoidal rule with n= 10. Work for 6 digit

A: Mathematically the derivative of a function is defined as f'(x)=limh→0f(x+h)-f(x)h. According to the…

Q: Having f (x) = 1 +e¬* sin(4x) and the interval [0,1] Apply composite Trapezoidal and Simpson's rules…

A: I have done by the direct method and trapezoidal rule and find the error by trapezoidal rule

Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin°x .…

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Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is ∫-π4π4sec2xdx

Q: The base of a three-dimensional figure is bound by the graph x = cos(y) + 1 on the interval [-n, r].…

A: Option(2) is correct answer.

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

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Q: Find Ahe radius and interval of canergene for Ne sanes 3n+2 he

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Q: 9. Using n= 8 approximate the value of cos(1+Vx )dx using (a) the Midpoint Rule, (b) the Trapezoid…

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Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is…

A: The position of an object,st=14cos4t-16sin4t on the interval 0&lt;t&lt;3

Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: From the equation, f(θ)=sinθcos2θ-(cot θ / θ) +1, what is/are the critical points?

A: Consider the equation

Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Find the length of the curve [x = eª cos(t) y = et sin(t) for 04 (Hint: You can simplify the…

A:

Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: (c) Integrate sin"uelog (cosu) . Where n is 482

A: Integrate the sinnuelog(cosu). Where n=482

Q: Evaluate fo (6+3 cos a) da using Trapezoidal Rule (n=2). O 12.43167 O 12.26896 11.78097 O 12.386125

A: The given problem is to find the approximate value of the given integral using Trapezoidal rule with…

Q: Find the egetion of the tanqent line on the interval (o,5) to co.1, 6.2)

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Q: Sketch the following, marking points of interest. Y = (*+2}(x+4}/(x+3) Y= 2 sin x+1 Y= sin (2x)

A: Given Y = (x+2)(x+4)/(x+3) Y = 2sinx+1 Y=sin(2x)

Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: See image below....

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Q: The value of [xe*dx by using the three-segment trapezoidal rule is most nearly

A: by trapezoidal rule

Q: 1. Use Trigonometric substitution to evaluate f dx. Hint: Ju? – a² let u a sece.

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Q: Solve the eaation on the interval. 2sin Đ =3(cos o t D

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Q: Compare the Trapezoidal rule and Simpson's rule app 4 x sin x dx

A: Given: An integral ∫0π4xsinx dx. To find: Bound for the error using the formula for each rule and…

Q: 1 Using the fact that 1 du = -tan (-) +C, which of the following is equal to a² + u? 2x dx? o 16+x

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Q: a) cosh (x) tanh' (?) = sechi! (?) find the "(?) In 1- i

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Q: Obtain the approximate answer for 2 cos(x )dx using the trapezoidal method so 3) that the maximum…

A:

Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

Q: Find the length of one arch of the cycloid x = 9(t – sin(t), y = 9(1 – cos(t)).

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Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

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Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x- 4 sin'x.…

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Q: Analyze the approximate value and the exact value for (7.2, 4.06) for the function z = x³y? sin(xy)…

A: Given below clear explanation

Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

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Q: Find the convolution of fix) = sin bx, g(x) = exp(-alx), a>0.

A: Convolution: Let and be two piecewise functions, then the convolution of them is denoted and defined…

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.