57. Use FTC I to show that x" dx = 0 if n is an odd whole number. Explain graphically.

Q: 9. z In(1 + x²) dx

A: As mentioned to solve only question number 9.Question number 9,Given,          ∫xln1+x2dx

Q: Use FTC I to show that x" dx = 0 if n is an odd whole number. %3D Explain graphically.

A:

Q: 20. Use u substitution to evaluate. S secrtant 1+secx dx

A: Evaluation of the indefinite integral by substitution method

Q: 70ot(*) e*dx e2x +1

A:

Q: 76. Use integration by parts to obtain the formula VT=* dx = +VT=x + 1 dx. 1 – x?

A:

Q: 53. Find the value of 1 dx using weddle’s rule. 1+x?

A: Weddle's law is a formula for solving numerical integration.

Q: 2. Count 1-e-x2 dx x2 -1 to an accuracy of 3 decimal places after the comma!

A:

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: 57. Verify that S2 yields the exact value of | (x – x³) dx.

A:

Q: 1 en (enx)+ dx (enx)?

A:

Q: 19. What is the equivalent value of *Vx+ Tdx 20. In evaluating (&+ Idx x dx which one is to be used?…

A: The solution for the above question is as shown below.

Q: 4-2x 33. dy dx 0 J 2

A:

Q: dy 2ху 3 Зу*, у(1) %— dx 112

A:

Q: iii. Sx coth-x dx.

A: (III) Apply the integral by parts rule, ∫u.vdx=u∫vdx-∫dudx.∫vdxdx Here, u = x and v=coth-1(x) As we…

Q: Sxe* dx

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: Evaluate x In x dx.

A: This is solved using product rule

Q: Evaluate exactly. In4 xe'dx TTTArial

A:

Q: Use the midpoint rule with = 2 to estimate 1 dx. Hint Ax = 2 m1 = and m2 = Answer 24 35

A:

Q: d -(In(5x + 4)) dx Find

A:

Q: Evaluate. (Be sure to check by differentiating!) | 16. dx

A:

Q: s there will be At) bacteria present in a certa tant. If 60 000 bacteria are present initially,

A:

Q: 2. Use reduction formula to evaluate the integral: sin xdx.

A: We have to evaluate integral by using reduction formula.

Q: 2. y = Arctan

A:

Q: zc)z (32- 5х) dx —

A: We have to find

Q: 70. Use the fact that (b*) = (In b) b* to prove that (ek*) = dx dx kekx. ||

A: Differentiation rules help to prove the required. The given fact helps to prove the required. Chain…

Q: 16 Evaluate x*In 3x dx correct to three decimal places.

A: Given that, ∫12x2ln 3x To find- The value of the above integral. Concept Used- The above integral…

Q: So Si S*x 1 су-х ху dzdydx

A: Let the integral be  I = ∫01∫x1∫0y-xxydzdydx 'I' can be solved directly by integrating individual…

Q: cln 2 In 5 e2x+y dy dx Jo 1

A:

Q: 2) у(и? + 1)du + (из — Зи)dy — 0 -

A:

Q: Use FTC I to show that x" dx = 0 if n is an odd whole number. Explain graphically.

A: Given: show that ∫-11xndx=0 if n is an odd whole number we know that  ∫xndx=xn+1n+1+c…

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

A:

Q: Find the antiderivative of sin(square root of 5x)

A: Consider the given function:

Q: dy 5. х dx - (1 + х)у %— ху?

A: The methods and formulas to find the solution of the Bernoulli equation help to find the required…

Q: 3. tan e de ) 71+ In cose)43

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: find dy/dn in5 フx 34+2

A: Since you have posted multiple question We solve only first question  for reaming question post…

Q: valuate. (Be sure to check by differentiating!) 1 dx, x - 3+7x 3/7

A: Evaluate the given integral and check it by differentiation. ∫13+7xdx, x≠-37

Q: 4. Describe in detail three separate ways to find /. Evaluate any two of these to show that they are…

A: I=∫x9-x2 dxUsing substitution method:u=9-x2du=-2x dxx dx=-du2=∫x9-x2  dx=∫-1u du2=-12∫duu=-12∫u-12…

Q: 9. For what value of k, k> 0, does (4kx-5k) dx = k² O 1 O 2 3 O 4

A: On solving this we will get

Q: Evaluate. (Be sure to check by differentiatingl) 1 dx, x# - 3 9+ 3x

A: To evaluate: I=∫19+3xdx Use the rule: ∫1xdx=ln |x|+C

Q: tan e = cose 6. 2 =1 t. 2+1= 2. 2. 5. 2.

A:

Q: Evaluate: ³²₁ [2³(x + y)³] dz dy dx

A:

Q: Q1: what is on (3x) SI2 dx x2

A:

Q: S tanx dx 5

A:

Q: Find integral 2  to 5    1/ sqrt  (x -2 ) dx

A:

Q: differen tiatin, de tomine dx リ= (aH) (xs) 5 (as) (x-+)

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: ~tu{S} o 1 In(y) dy de

A: We have to find the double integral

Q: Explain why de 1. dx 1. Va³+5

A: Comparison test for Integral

Q: Evaluate 18z dz dy dx. Enter your answer as a numerical value in decimal form.

A: