If IN = frNe-2= dx, show that IN +IN-1, and hence evaluate f r*e-2" dx = -

Q: Use Green s theorem to evaluate the give (y² dx + 8xy? dy)

A: In this question we will use basic of calculus i.e concept of integration. We will use green's…

Q: Find p, q if f" f(x) dx – f(x) dx = S, f(x) dx. - (Give your answers as whole or exact numbers.) p =…

A:

Q: HiWi Put a -af T ±aN #N If rit) =É é costi + e sint j +2 K

A: Given: rt=etcosti+etsinti+2k.

Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

A:

Q: How would you choose u when evaluating x" cos ax dx using inteeration by parts?

A: Given integral is ∫xn cos ax dx

Q: Compute the exact value. 2 dx 2.

A: Simplify the given integral using limits.

Q: What is ſ e2x dx? 1+ex

A: Given :                      ∫e2x1+ex dx     Substitute u = ex+1  ,  dudx = ex…

Q: dy is let y = (sin æ)*an 7 then dx

A: Given

Q: If (x – k)³ dx = §,x³ dx , find k? %3D -

A:

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

A:

Q: Obtain a-(In x)? dx.

A: Given,  ∫x-5(lnx)2dx

Q: of e dydx

A:

Q: の1) (のの) (めみ) Cn %3D Cnt = %3D antt San So,itis increa Sing. @dn=

A: dn=n32n! On simplification, we get dn=n32n·2n-1!=n22·2n-1! Now,…

Q: 22. Evaluate So Si S dx dy dz.

A:

Q: What is the value of , x(x + 1)+ dx ?

A:

Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: evaluate Fhe In tegral 子 dx

A:

Q: Evaluate x In x dx.

A: This is solved using product rule

Q: Use symmetry to evaluate the followingintegrals.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 3 ex dx = e3 - e, use this result to evaluate Given that 5ex + 6 dx.

A:

Q: "4 rseco sin 20 dp do d0 0. 0,

A:

Q: 2sinh cosh -dx 3cosh? * 2

A:

Q: d Verify coth x = - csch² x. dx

A: Differentiation is the rate of change of some variable with respect to the other variable. If a…

Q: dx Evaluate Зх — 12

A: Solution:

Q: Use a computer algebra system to evaluate theintegral. Compare the answer with the result of using…

A: Find the value of the integral ∫11+x3dx. Evaluate the integral as follows. ∫11+x3dx=∫3u21+udu…

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: dy let y = cos(In(cos(x))), then is dx

A:

Q: Show that esin(x²)dx < e– 1.

A:

Q: Show that: (e) (VF) = 1 dx

A: Derivative of a function xn: ddxxn=nxn-1                               (1) Given function is: f(x)=x…

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

A:

Q: d tanh (u) du Sech (u) dx dx

A:

Q: o evaluate (In x)² +3 dx,

A: answer is in next step  option C is correct

Q: (e) S, In|x| dx.

A:

Q: dy _ 1 dx y-x 6.

A: 6) Given:             dydx=1y-x               dxdy=y-x                dxdy+x=y This is in the form…

Q: How's f', and g'(x) used in composites d/dx for deriving

A:

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

A:

Q: if x = acos30, y = asin30 , find /1 + 2 dx

A:

Q: Solve the problem. Suppose that fis continuous and that " H2) dz-0 and S Ka) dz = 4. Find - 60) dx .…

A:

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: Evaluate az+1)in(d.r+1)dr. 1 dx.

A: The integration function is ∫14x+1ln4x+1dx

Q: Show that for B > 0, Be-Ba dx = 1. |

A:

Q: Evaluate 1 dx, x = 0, x = 1 1- x

A: Using beta and gamma function.

Q: Evaluate e (r- 2|) dx if it exists. If it does not exist, explain why.

A: To evaluate: ∫-12x-2|x|dx

Q: dy Find if y = In|9 + x|. dx

A:

Q: 3 Given that ex dx = e³ – e, use this result to evaluate 7ex + 4 dx.

A:

Q: If (Mesin(2x) dx = eSin(2x) + C, then the M is equal to-

A: We will differentiate both sides w.r.t 'x'

Q: find using Serie s リ2 dx "I+X 2

A: As a first step, we need to obtain a series for the integrand.