If P(X > a) = –, then a is equal to: 16'

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

A:

Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

Q: Evaluate L e* dx dy by using trapezoidal and Simpson's rules.

A: Given that, ∫02∫01ex+ydxdy By trapezoidal rule, ∫abf(x)dx≈h2f(a)+2fa+b2+f(b) where h=b-an…

Q: I am having trouble evaluating ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above…

A:

Q: Evaluate e Cos I dx with tolerance e = 0.05 using the Composite Trapezium Rule. %3D

A: Equation is f(x)=ecos(x).The value of the table for x and y x 0 0.25 0.5 0.75 1 1.25 1.5 y 2.72…

Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

A:

Q: To evaluate fx (cos x2)e* dx, use integration by parts. What is the best choice for u and du?

A: Consider the provided integral, ∫ xcosx2ex2dx Evaluate the provided integral. Apply the substitution…

Q: sinh x – 1 dx cosh x

A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: sinh x – 1 dx cosh x

A:

Q: 2.f(t) = cosh wt sin wt

A:

Q: (b) Calculate fe" con(r2) dz using integration by parts as many times as necessary.

A:

Q: Q1-If x= cot- VE, y =, find d²y dx' dx2 at t = 2.

A:

Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…

A: Answer

Q: How would I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

A:

Q: Without integrating, explain why: S, ?)°dx = o x(1+ x* -2

A: To show:     ∫-22x1+x22dx = 0 (without integrating)

Q: 3- show that the diff. equ. is homogeneous and Salve it (2x +34) dx +(y-x)dy = a

A: In this question we have to solve the differential equation.

Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

A:

Q: How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

A:

Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

Q: Show that the antiderivatives are equivalent.                                                     ∫…

A: To show that ∫3x21-x6dx = arc sin x3+C Substitute  u = x3. Then                  dudx=3x2du  =3x2dx…

Q: Given tanh(x)+ tanh ¯' (y) = 1, show that, 1- y? 1 – x² dy dx

A: Formula,ddxtanh-1x=11-x2Note- Since multiple questions are asked, I am answering the first question…

Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

Q: Find the most general antiderivative , verify answer by differentiation  g(x)=7sin theta/3

A:

Q: d cosh z =sinh x dz صواب ihi

A: Use the formula of coshz and sinhz in terms of exponents.

Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: Given Approximate value of the integral by Simpson's rule(Vs) = 0.3480 Now we will find the actual…

Q: dx 5 + 4 sin a

A:

Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

A:

Q: The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given by…

A:

Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

A:

Q: 2.f (t) = cosh wt sin wt

A:

Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate…

A: The given integral ∫1e2ln x dx, three rectangles and left end points.

Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

A:

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: What is the derivative of r(t)=e^(4t)costi+e^(4t)sintj+e^(4t)k

A: Differentiate both sides with respect to t.

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

A:

Q: dy 4. If y =cosh( 4 tanhx) dx

A: As per your query the answer of the question no 4 is given in the next step.

Q: If y = tanu, u =v--, and v= In x, dy at x= e? what is the value of dx

A:

Q: The approximate value of| dx by using Simpson's rule is 0.3639, then the error in the approximation…

A: Approximate value of ∫161x4dx by using Simpson's rule is 0.3639 To find the error in the…