Find Sea)ax Jf(x)dx if = 56 foR X

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

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: 2x Ex FIND THE DERIVATI VES %3D

A:

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

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

A:

Q: dy satisfies dx? 2 iven by

A:

Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

A:

Q: Evaluate f S S," x dz dy dx

A:

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

A:

Q: Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

A: We have to find the definite integral using substitution method In place y^2 =t                2y dy…

Q: Using an appropriate substitution, 3 the integral S dx equals: /1-4 (х-1)2

A: Here we have to evaluate I=∫31-4(x-1)2dx

Q: find the critical points:

A: Given function is  and the interval isThe critical points of a function are obtained when the first…

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: Use two different methods to calculate dzu/ar if u = /x² + y². = est, and y = 1 + s² cosz. IUse two…

A:

Q: af Find of f (x, y) = sin %3D dx 1+ Y COS 1+y () Option 1 sin 1+ y 1+ y Ontion 4

A: Partial derivative of a function in several variables with respect to one variable is calculated by…

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

A:

Q: By using Trapezoidal rule, the value of "h" in evaluating ((x² – 2x +1)dx, by taking 8 subintervals…

A: The value of h to evaluate the integral  is 0.25 option (a) is true.

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

A:

Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

A:

Q: Use the substitution formula to evaluate the integral. T/16 (1 + etan 4x) sec 2 4x dx 4e

A: Given that ∫0π161+etan4x sec24x dx ...........................(i) Substitute u= 4x  dudx=4 ⇒dx=du4…

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

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: 9. Use integration by parts to show that pP+1 ]n°(x) |aP In°(x) dx p+1 p+1

A:

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

A:

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

A:

Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: s continuous on la,b), then d f(x)dx = f(x) dx A) True B) False

A:

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: Use implicit clifteren tra fion to find * for the fol llving x*y+ 3xy-x = 3

A: The given equation is x2y+3xy3-x=3 To find: dydx

Q: 5. Use integration by parts to evaluate dx. (x+1)2 Hint: Choose u = x.

A: Given that ∫xx+12dx∫xx+1-2dxNote : integration by parts∫fxgxdx=fx∫gxdx-∫dfxdx∫gxdxdxfx=x…

Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

A:

Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .

Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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: Find the most general antiderivative of f(x)=6e^x+5 sec^2(x), where -pi/2

A: Please see the answer below

Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

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: Given that 1 dx = and x2 dx = , compute the integral. x dx = 4 2' 3' La - 20?. (1 – 2x)³ dx

A:

Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

A:

Q: Using Simpson's method Vx dx for n=4 is equal to

A: We have to evaluate ∫01xdx for n=4.

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: Show that the antiderivatives are equivalent.…

A: ∫6/(4 + 9x2)  dx = arctan 3x2 + C or arccsc √(4 + 9x2 ) / 3x + C We need to show that the…