olve the equation on the interval 0s0<2x V2 sin0- sin 0 = 0

Q: Find the integral. er sin(5x)dx - IT

A: Known integral formula:

Q: 2 y = 0.38 sin x-.49x²

A:

Q: The curve y = tan x crosses the line y = 2x between x = 0 and x = pai/2. Use Newton’s method to find…

A:

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: Estimate the root of 2 cosh x sin x 1, using the secant method, with an accuracy of 4dp. Take 0.4…

A: Image is attached with detailed solution.

Q: 3.§ sin* 2 x sin 4 xdx

A:

Q: Use Newton Raphson method to obtain a root to 3 decimal places 1.   x^3-5x+3=0 2.   sinx=1-x

A:

Q: Find a root of the equation 3x + sin(x) - e* = 0 using Newton Raphson Method. Consider initial guess…

A: Let fx=3x+sinx-ex Then f'x= 3+cosx-ex Given that x0=2·500

Q: 2. Evaluate J dx (cos³x sin³x)

A:

Q: 3. S. 2 cotx-3 sin²x dx sin x 4. (2x2+x dx x+1

A:

Q: Q#2 (a): Find root of the equation 3x + sinx – e* = 0 by secant method correct to six decimal Places…

A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

Q: Find the two values of 0 in the interval-180° <0<180° such that sin(0) = -0.40. %3D Enter your…

A: Given the trigonometric identitysinθ=−0.40 And θ varies through −180° to 180°

Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

Q: sin 2ydy 4 – 3 cos 2y

A:

Q: Compute integral. sin(x) cos(x)V4+sin? (x) dx. 2.

A:

Q: of the tangent line to the sine function at the origin. y y= sin(7 x) values with the number of…

A:

Q: Using secant method, detemine a root of sin Vx - x with initial guesses xo = 0.5 and x, = 1…

A:

Q: Evaluate the definite integral. ∫0 π/2  Cos x Sin (Sinx) dx

A:

Q: sine da Seco co?o

A:

Q: i ösin° ( 4x) cos (4x) cos" (2x)dx

A: To Solve the definite integral:∫0π45sin3(4x)cos2(2x)dx

Q: Find the integral of sin(8x)sin(x)dx

A: on doing integration

Q: 4. sinx 1-sin² x dx

A: We have to find the value of the given integral ∫sinx1-sin2xdx

Q: Complete the integration: 1 1 Scos (2x)dx = sin 2x -sin 2x + C Determine the value of "?".

A:

Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let x₁ = 2 be the…

A: answer is in next step

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Recall that the linear approximation of a function y=f(x) at x=a is given by y=f(a)+f'(a)(x-a) Here…

Q: Find the equation of the line tangent to the graph of f(x) = -2 sin (x) – 1 at'x = =. (Enter an…

A:

Q: Apply Newton-Raphson method to determine a root of the equation cosx- xe^x correct to three decimal…

A: Let us consider an eqaution f(x)=0 with the initial point x0 to determine the roots of the equation…

Q: Use Newton's method to estimate the solution to sin(theta) = 1- theta/2 up to four iterations.

A: Given function is: f(θ)=sinθ+θ2-1 Rewriting function in other variable: f(x)=sin x+x2-1 Newton…

Q: Solve the integral: (1 – sin 0) do dx

A: Consider the double integral ∫05∫0πx(1-sin θ) dθ dx To evaluate the integral, first evaluate the…

Q: +2 dy x2 + sinx – y = 0 dx

A:

Q: Find the linear approximation to h(y) = Sin(y+ 1) at y =0 Use the linear approximation to…

A: This is a problem of linear approximation.

Q: S sin x In(1 + sin x) dx

A:

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1 Differentiate f at x = 0.5 using 5 point formula. Also…

A:

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given that y=sin-1(ex). We need to find the absolute and local extreme values of the above function.…

Q: 2. Solve for general solution using exact method. (cos x cosy – cotx) dx – sinx siny dy = 0 %3D

A:

Q: Find the root of the equation Cosx-x' = 0 near to 0.5 using Newton-Raphson method correct up to 3…

A: To determine the root of an equation using Newton-Raphson method, first choose an initial value x0…

Q: Solve the Indefinite Integral. S sin Vædz

A:

Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: Find the trigonometric integral ∫sin x cos4 x dx

A: Consider the integrals: ∫sinx·cos4xdx…

Q: Find all solutions to cosh z = i sinh z.

A: To find all the solutions of the below equation. coshz=isinhz

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -pai to x =…

A: given

Q: Find the root using newton raphson method for f(x) = sin(x) − x²

A: Given function is f(x)=sin(x)-x2 From the given equation, it is clear that 0 is one of the root of…

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: sin(5x)dx X sin

A:

Q: Find the trigonometric integral ∫sin2(x/2)  dx

A: From the given data:

Q: Use trigonometric substitution to solve the integral Jx*V1+x² dx

A: Note the results :     (Identity)

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

A:

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: Use Newton's method to approximate a root of the equation 5 sin(x) = x as follows. Let x1 2 be the…

A: The given equation, 5 sin(x)=x

Q: What is the value of the integral S sin(6x) arctan(sin 3x)dx? 2 c) 6 а) 3(т — 2) b) d) 6(т — 2) е) п…

A: