Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

A:

Q: Evaluate e sin x cos x dx using Simpson rule with h 20

A:

Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin-1 5x)…

A:

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

A:

Q: Evaluate the following 1, the integral from 0 to π/2 of Cosx/(1+sin^2 x) dx 2, the integral from…

A: 1). the integral from 0 to π/2 of Cosx/(1+sin^2 x) dx   = arctan(sin(x))    Answer: π/4

Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

A:

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Use TWO different methods to find the PS of the IVP: sin x + y cOs x = 0 ( y(7/2) = 2020

A:

Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)<0 and f(b)<0.…

Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

A:

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Use the substitution u =   /2  − x to evaluate the integral

A: Let I=∫0π2sinxsinx+cosxdx                    ⋯⋯1 Using property of definite integral…

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: Find dy/dx for following functions. 1) y = csc-(e2lnx) + sin-1(2lnv3x)

A: it is given that,  y=csc-1e2lnx2+sin-1(2ln3x) we have to find dydx=?

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

A:

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

A:

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Evaluate the following 1, intergral from 0 to π/2 of (Cosx)/(1+sin^2x) dx

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: Evaluate the integral. sin 8x cos 9x dx

A: Given that ∫sin8xcos9xdxSolution :…

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

A:

Q: Evaluate the integral sin x dx (2 + 3 cos x)2

A:

Q: Differentiate the following finction f(x)=sin(3 ln(x))

A: Given that the function is       f(x) = sin(3 ln(x)) We have to differentiate the the function f(x).

Q: Find by implicit differentiation. 3+ 6z = sin(zy') dy Answer: dz

A: Solution is in step 2

Q: Evaluate the integral ∫sin (2t + 1)/cos2 (2t + 1) dt

A: Given information: ∫sin2t+1cos22t+1dt

Q: evaluate the definite integral.

A:

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: f(x) = cos (In (3x))

A:

Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

A:

Q: Given the integral sin(3x + 5) dx cos(3x + 5)

A:

Q: Compute L {sin(2t)e"}.

A:

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

A:

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

A:

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

A:

Q: find integral 2) S sin?xdx dx cos³x

A:

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

A:

Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

A:

Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

A:

Q: Q/ Find to the following functions: dx 1- sinh (x² + 7x + 12) 2- cosh²(17 – 4x²)

A:

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫x sin (2x2) dx, u = 2x2

A:

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

A:

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…