Prove the following result: Lf(at) = 1 S F a a Evaluate L(cosh(5t)).

Q: dy +y = zy dr

A: Given equation is: xdydx+y=xy3

Q: Determine weather the statement is true of false. Explain your answer.

A: Consider the given differential equation dydx=1x2+1 Use separation of the variable method to find…

Q: a) Evaluate the following integrals »f xe*dx 2) fx* sinx dx 3) x sin 2x dx

A: According to the guidelines of company I can only answer first three subparts of the question. For…

Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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Q: T 4. Approximate the integral fo x cos xdx with n = 6 using the Composite Simp- son's rule.

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Q: Find the indefinite integral. (8ti + j + k) dt + C

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Q: b. Find the value of V1- 0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

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Q: 8 cos" 2πt dt

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Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: 2 Evaluate the definite integral 16sin(t)cos (t) dt.

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Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

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Q: Find cosh a In(sinh r)dr.

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Q: - Evaluate the integral dx using Simpson's th rule e* – 1 3 -

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Q: what is the integral of e^(-2a|t|) from 0 to w

A: Given integral: ∫0we-2atdt

Q: ) Evaluate the following integral: S V2 + sin 3t cos 3t dt

A: We have to find solution of given integral.

Q: Prove that for all r € [1, 00), – sinh (- |cosh-(x)|) = vVI² – 1.

A: We know that: Cosh-1x=logex+x2-1  and  Sinhx=ex-e-x2. And, Sinh-x=-Sinhx. Therefore,…

Q: a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that…

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Q: 1. Compute the following integrals. (a) sin (e) dx. 4 dx. - (b) x2

A: we have to calculate integration

Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: Evaluate the following integral T/3 sin x In(cos x) dx

A: We have to prove

Q: Compute an approximation to the value of Le-x*dx a) using Simpson's Rule b) using Simpson's…

A: The composite Simpson's rule approach is a frequent way to deal with issue. To accomplish this,…

Q: Q1: Evaluate the following Integration: a) ( In(x²+x)-Inx-en3 dx b) S; sinx Ine(x+1) 1-cos²x

A: Answer (a): To evaluate this integral, apply the logarithmic properties : And, And, And, And,…

Q: If the definite integral of (1 + sin y)dy with lower limit equal to zero is π+2, its upper limit is…

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Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

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Q: (e) /a (с) dx e2x 2.х

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Q: Evaluate the definite integral. T/4 (sec t tan t)i + (tan t)j + (2 sin t cos t)k dt 0.414i + 0.3466j…

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Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: Evaluate the integral e'sin e) dx 1- In 2 2 u +3 u + C + C +C cos(e") + C COS -2*+2x + C 21 21

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Q: Question 6 Estimate the integral 1 dx by Simpson's rule using n = 8. Vx3 + 4 a) 00.9361 b) O1.0212…

A: given integral :

Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

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Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: Calculate L4 for f(x) = 42 cos () over L4 = %3D

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Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: b. Find the value of V1-0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

A: We apply Simpson 1/3rd rule it is given that six sub intervals must be mentioned so in the interval…

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

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Q: Find the indefinite integral. cos t dt sin t

A: Consider the given indefinite integral, ∫cos5tsin tdt use the trigonometric identity, cos2x=1-sin2x…

Q: Q1. Use the Fundamental Theorem Of Calculus and the Newton-Leibnitz rule to answer the following: 1.…

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Q: 3) Evaluate the following integrals. a) | cos(tan(x)) sec (x) dx

A: Given that ∫cos(tanx) sec2x dx first let us simplify and then integrate

Q: Evaluate the integral cos (x) sin(x) dx 13 using the substitution u = cos(x). cos(x) sin(x) d.x ,13…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the definite integral. integral (lower 0, upper 3) t^3 sin(t^4) dt  =

A: We have to solve the definite integral

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration

Q: 1. Evaluate the following integrals: g) . dx sin-1 x V1 – x2

A: Since you have posted more than one question we solve the first one for you. For the remaining…

Q: n²(ln(ar)) dr,a>0 J 2r In(ax) a.

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.