Evaluate [ = dx. xVx* -1 (a)

Q: Compute the derivative of the function F (x) = L evi dt.

A:

Q: Use implicit differentiation to find dy/dx in x3 - xy + y3 = 1

A: We differentiate both sides with respect to x

Q: find dy / dx by implicit differentiation.

A: In implicit differentiation, on differentiating y, we use dy/dx.

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

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

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Q: Express (3*) dx as the limit of a sum. 1

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Q: Find

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Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: 23 dx V25 – x2

A: We integrate the function using trigonometry substitution.

Q: Integrate O sinh 2x dx

A:

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

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Q: d VE evedt dx d -S Intdt dx 1

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Q: 14.Use a substitution to evaluate / aVx+1 dx rVa+1 dx. Show all details of the process.

A: To solve- given integral by substitution  method.

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

A: Given,  ∫x-5(lnx)2dx

Q: The integration of dx is 4+x²

A: The given integral ∫dx4+x2 can be evaluated as, ∫dx4+x2=∫dxx2+22                =12tan-1x2+C…

Q: Use implicit differentiation to find dy/dx. In xy-y = 3

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Q: -1 Integrate Jxsin 'dx

A: To evaluate : ∫01x sin-1x dx

Q: 2 dx =

A:

Q: Integrate Jo tan h x dx

A: Use substitution method for integrate

Q: Find e-ax dx } first integrating and then transforming result.

A: Here we find Laplace transform

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: Integrate: S sin³x cos³x dx

A: ∫tndt=tn+1n+1

Q: Find the indic ed derivative. dz x2 for z = x2 dx 1 - x - 2x2 dz dx

A: Formulas:

Q: Integrate: ∫ 3cos(2πx) dx

A: The given integral is ∫ 3cos2πxdx.

Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Find the indefinite integral.

A: Use the substitution method and consider x2 as u. Differentiate both sides of u=x2 and substitute x2…

Q: integrate (2 + x^2)/x^1/2 dx from 1 to 4

A: to find I=∫142+x2xdx

Q: Integrate x sqrt of (x+4) dx using algebraic substitution

A:

Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: Integrate dx/(x+1)(x^2+16) from 0 to 1

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Q: Integrate f dx using integration by parts. x+1

A: Please refer the attached image for complete solution.

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

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Q: Evaluate integral x^2e^-x^3 dx

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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 ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: integrate x^4cotx^5 dx from 0.4 to 0.8

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Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: Integrate: Jez sin(3x) dx

A: Solve the integration by substitution method

Q: Evaluate the integral.

A: Let the given integral be y - y = ∫sin-1x2dx            ...............(1)Let,x = sinθ…

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

A: Using beta and gamma function.

Q: Integrate x?dx

A:

Q: Integrate completely

A: Given,             ∫2x+12x-53dx

Q: Verify the differentiation formula.

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Q: Integrate: Sx e* dx.

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Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.