(a) Va? – x² dx .2 - (Ъ) V1 – x² dx

Q: Evaluate: (answer in fractional form så S sinº x dx 0

A: To find the value of given definite integral ∫0π2sin6xdx

Q: 1 dx. 3 Evaluate x(lnx 8.

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Q: dy from the equation 3xy? + 42- Y-5 dx Evaluate = 11 when X = 1 2x? –1

A: 3xy2+4yx-y-52x2-1=11 when x=1

Q: Differentiate. y= In [(x +2)° (x + 5 (x+ 7)°] [In [x+ 2)° (x +5)*(x + 7) ]] =O dx

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Q: iate ſ In(x + v1 +x²)dx

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Q: -п/8 S sec? (2x)dx

A: We have to evaluate the definite integral: ∫0π8sec22xdx Assuming, t=2x Then definite limit will also…

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

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

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Q: 2 csc In x dx

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute…

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-S cosh? Vx dx x csch vx

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Q: -2 Evaluate dx ех

A: The objective of the question is evaluate the definite integral.

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

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Q: Q2- Evaluate 1- L,(x + 2)5e-(*+2)dx.

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Q: 3. X+1 (tah dx X-1

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Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the integrals in Exercises

A: In some cases a substitution can simplify an integral to a standard integral. For example the…

Q: d) S 3x²e*dx e) 2t?Vt3 +1 dt

A: evaluate the integrald)∫3x2exdxe)∫022t2t3+1 dt

Q: 2 S (a+ dx x - х — а

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Q: - 1 dx

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Q: cosh(lnx)dx 4. f 5. [* cosh vxdx 6. Jo Sm 10 4sinh? () cosh ) dx

A: Solve the three questions.

Q: 3. S dx (9-x) √x

A: Student has specifically asked for the solution to the question (3). That is why, answer to that…

Q: 2х + у dy 3+ 3у? — х dx 3.

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Q: 6. §, (x +1)? e*dx •4 dx х —1 7. 2 8. x²cos2xdx

A: Note :  As per our guidelines we are supposed to answer only one question and 3-subparts. Since you…

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: Find the values of a that make: ja- |(x– 2)dx = 6

A: Answer

Q: 5. fxe* dx 7. S (In x)² dx 9. Sx sec? x dx

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

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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 In (x) dx

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Q: dx x? – 4x + 5

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Q: b) S Ti dx x2+1 V.

A: Given,          ∫xx2+1dx

Q: |(er + Se") dx 42. (2e- 3e 2) dx 41. In 3 43. e dx 44. e* dx -In 2

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Q: Evaluate [(x² +2) dx , using Trapezoidal rule, by taking N = 8.

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Q: Kindly sotve por : Dx (In | v | ) = Dx ((tan (3x) - In | 2x| + ( x³ - In | e|) - In | Inx | )

A: On differentiating Lhs: ddx(ln y)=1y.dydx on differentiating Rhs: ddx( tan(3x).ln|2x| +…

Q: B4. Evaluate the integral [(3x² - ª ++5 x -6) 4 +5 /x – 6) dx .

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Q: -133x So 33x dx 0.6698 0.6670 0.6671 0.6699 O

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Q: In (x) -dx is equal to x2 The numerical value of

A: Given is an integration and we have to find it's numerical value. Here, we use the Integration by…

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

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Q: V1 - (In x)² x ln x VI dx

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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: how that 1 dn v2

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Q: Explain geometrically (without calculation): x/n dx = 1 x" dx + (for n > 0)

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Q: d. X 3 Vt4 + 1dt dx -x

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Q: Q2- Evaluate 1- L,(x + 2)*e=x+2)dx.

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Q: 5 |V25 – x² dx Compute the value of

A: Given: I=∫0525-x2dx we know that ∫a2-x2dx=x2a2-x2+a22sin-1xa+c                                  ...1

Q: dy Calculate dx2 y = x4 8 In (x) 960 16 dy dx2 - 7

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Q: 3 Differentiate the expression (x + y )" with respect to x. (Use D for 2). dx

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