In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

Q: In(x) dx Vx

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Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: A spring has a natural length of 15 inches. A force of 10 Ibs. is required to keep it stretched 5…

A: for F = 10 , x = 5

Q: Apply the method of integration by parts to (In=) In æ ) (--) e dx dv

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Q: Evaluate the double integral : (y³ – 12x) dx dy -

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Q: 5x2 dx et

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Q: S(1 - In =) 1 dx x2

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Q: tan- Find -dx using integration by parts. x2

A: The given integral is: I=∫tan-1xx2 dx

Q: 4 (1+2 In x)* 6. J dx б.

A: We have to find

Q: What is the value of the integral ∫2−2 max [1,x2] dx ?

A: This question is related to integration.

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: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: x² sin 2x dx

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Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

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Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

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

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

Q: The general antiderivative determined by - x² - 3x +2 is dx

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Q: 2 3 хе dx

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Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x -dx, in six…

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Q: dy )"ح.

A: To solve the integral using the integration by parts: ∫y2·eydy Solution: Integration by parts states…

Q: To calculate x²e*dx dp, integration by parts is the best integration technique to use. O True O…

A: Explanation of the solution is given below...

Q: Find /- tan- x -dx using integration by parts. x2 ITM

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Q: valuate the definite integral: 1 (sec-1 x)² dx xVx² – 1 -

A: We  have to solve the improper integral

Q: O Integrate In 2x dx by using integration by part.

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Q: JECT tinoM Use integration bu ax e cosbx dx

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Q: dx y.= dy y arctan (-x 2a

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Q: dx Q2. Integrate

A: Given,I=∫1x2+15dx Consider x=tanu and u=arctan(x) then, dx=sec2udu…

Q: 1 a) x²e-x dx

A: Use the formula of integration by part and finally put the limit  to got the answer

Q: ] Integrate by parts to show that Vx dx = 2e4 - e* dx. ex. е —

A: To evaluate the given integral choose  √x as the first function and ex as the second function and…

Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: use a geometry formula to find the exact value of the definite integral.  5 dx on interval[-2,6]

A: Question is to find the exact value of the definite integral 5dx in the interval [-2 , 6 ]It is…

Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

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Q: Su+1 dn th-2

A: I =   ∫135x + 1x2 + x - 2dx    = ∫135x + 1x2 + x - 2dxWriting5x + 1  = A (2x + 1) +BOn solving , A…

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

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Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: What is the value of the integral ∫2−2 max[1,x2]dx ?

A: Value of the given integral is 2x [1- ((x^2) /3) ]

Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

Q: Se²(x² + 2x dx by using the integration by parts. Q4 Evaluate ,2x

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Q: a) Evaluate 1| dx by using integration by parts.

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: (0.2t25x+3x²) dx

A: We have to find the value of ∫050.2+25x+3x2dx using the Trapezoidal rule We take that the number of…

Q: dx 1+e2*

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Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3, y(0)=2, h=0.3. The objective is to evaluate y(3) by using Euler's method. The…

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

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Q: y

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Q: Evaluate the integration - 1 I = cos(3x)– 5 dx with h=0.4, Using 3/8 Simpson Rule. Write your answer…

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Q: O Use integration by part ax Cosbx dx

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