Evaluate the definite integral. (4y° - 3) dy 8. 2. 1 - (4y° - 3) dy = (Simplify your 8. 9. 2. -1

Q: Q: 1. Find the value of the following integral: sin vi dx using Simpson's rule when n = 8.

A:

Q: A particle travels along the x-axis such that its velocity is given by v(t) = t0.5 sin (2t − 3).…

A:

Q: 7 sin°(e) cos"(t) dt

A: To evaluate the given definite integral

Q: Find the value of the constant A so that y = A sin 7t satisfies the equation + 2y = 4 sin 7t. dt2…

A:

Q: T/2 e2x sin x dx

A:

Q: x dx x² + √√x². The integral - sine de SSH 1 + cose sece tane de sece - 1 sec²0 do 1+tano cose do…

A:

Q: S 5 sin(3x)e2cos(3r)dx

A: Solve integral by substitution method:-

Q: 04: S+* + 1)sin z dz =

A:

Q: T/2 S sin? x cos5 x dx

A: Topic = Integration

Q: •T/4 sin (4x)dæ S. 2e7"dx

A:

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: If y = sin?t+ tant, x=- In(- cost) - e sinr, find the value of y' when t==. 4 6 A 2 2 2/3 В 2-Vze 2…

A: Use dydx=dydtdxdt to simplify.

Q: After integration by parts we have e70 cos(80) d0 e70 sin(80) d0.

A: Explained below

Q: f (t) = sin? 4t + cos? 4t 4+s А. s2 +16 С. s2 +32 В. s(s2 +16) D. s2+16

A:

Q: d's -4 sin 2t dt? „s'(0) = 100,s(0) = 0 %3D

A: Given data:     The given differential equation is: d2s/dt2=-4sin[2t-π/2]. The first given condition…

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

A:

Q: VE-1 x= sec?t b) Find for y = dx sint

A: y=t-1sintDifferentiate w.r.t 't'dydt=sint·12t-1-t-1…

Q: Q1/: Evaluate the Trigonometric integral m/4 V(1+ tan?x)3 dx -a/4

A:

Q: Q1: Find dy/dx for the following functions (solve four only):- 4) y = cosh[sin-'(x²Inx)] (5) y =…

A: Here are the step by step solution of the given problems:

Q: 3. Give the third approximate value for the equation y = x* – sinh-'(x) closest at x1 = 2.5 A.…

A: Given that, the function is fx=xx-sinh-1x. It is known that, the Newton's Raphson method is…

Q: Q9 The definite integral 4 2T(T – x) (cosx – sinx )dx 0. represents

A:

Q: 1 y Solve the integral: cos -dy dx - T/2 Jo

A:

Q: 3. Solve for fe)(r) given that f(r)% = sinh(3r)

A:

Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: 2. S Find L{sin³ t}, L{e²t sin³ t}.

A:

Q: L{e_t (3 cos 6t 5 sin 6t)}

A:

Q: 4. f(t) = (e^(10t)) sin(2t) 5. f(t) = (e^(9t)) sinh(5t)

A:

Q: WIs the equation e sinx+x-2=0 has real roots?. ( 3r

A: As Multiple Question are given, I will only solve the first one : We are given : exsin x+x-2=0 Now,…

Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

A:

Q: Solve the following DE: a. (2x + 2y + 1)dx+ (x+ y-8) dy = 0 %3D

A:

Q: d) r- cos r + +3r = 4r3. %3D

A: the given implicit function is: x-cosx2+y2x+3x5=4x3 we have to differentiate the given implicit…

Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: Find the value of -4t e cos(4t) dt.

A:

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

A:

Q: '/2 Q4/ Find the Definite Integral cot 0 csc 0 de

A: Given: I=∫π4π2cotθcsc2θdθ...1 Use the substitution method to calculate the integral value.…

Q: Solve the differenttal equat on 1y +dy_64=12x-50 Sin 2x dx? doe

A:

Q: f(t) = 8 – 15 | "sin5r f(t-t) dt

A:

Q: (a) Find dr dy given that x²y + sin xy = 0.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q5. Find the general solution for the following first order ODE a) = sin (-4x) dx b) + 7y = e-2x

A:

Q: Q) Find the general solution. dy sin-1x Iny dx II

A:

Q: (b) Evaluate the given trigonometric integral sin r dx (x² + 1)(x² + 9)

A: The given integral is ∫-∞∞sinx(x2+1)(x2+9)dx. It is of the form ∫-∞∞f(x)g(x)sin(nx)dx. To solve this…

Q: evaluate the triple iterated integral.

A:

Q: dy 6. For parts (a) and (b) of this question, find Simplify your answer. dx (a) y = e® Inx

A: Derivative: y=tanx1-cosxddx(uv)=v.ddx(u)-u.ddx(v)v2

Q: O Find the approximations T10, M10, and S10 for 10 sin(x) dx. (Round your answers to six decimal…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Calculate SN given by Simpson's Rule for the value of N = 6. I cos(2x² ) dx (Round your answer to…

A: given the expression is , SN given by simpson's rule for the value of N=6 ∫01cos(2x2)dx

Q: J ? x sin 2x dk

A: This integral can be solved by the method of integration by parts which is given by

Q: Q1: Solve the following integral. dx 1 + 2**

A: We evaluate given integral