nterval est Value ign of h" (x) Conclusion

Q: 5. S sec(3x) tan(3x) dx

A: formula:∫ secx tanx dx =sec x +Cwe are given;I=∫ sec(3x) tan(3x) dx3x =t3 dx =dtdx =dt3

Q: lim x approaches 0 .............. (sinx)^2

A: Given:              limx→0 sin x2 Plug in the value: x = 0             =sin02

Q: -X -dx

A: We know, ∫uv dx = u∫v dx - ∫ddx(u)·∫v dx dx           (integration by parts) ∫1a2-x2 dx = sin-1xa +…

Q: cosh (x – 3) dx 2 '8 – cosh² (x – 3) х In x dx

A:

Q: integral

A:

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A: Given integral is

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A:

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A:

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A:

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A:

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A:

Q: 1. Find the first derivativ

A: Given that,

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A:

Q: True or False. 1. Integral calculus- is concerned with calculating areas bounded by curves, volumes…

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Q: Calulate thi ntegrul 17 3-49

A:

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A:

Q: limit Sin @2@) 0so ton Cs0)

A: solution

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Q: sechx+cshx b) prove that e2x cshx-sechx

A:

Q: Definite integral

A: Given :Definite integral

Q: x' sin (tanx*) -1 Integrate 1+x

A: Introduction :

Q: Topic: Integral of Hyperbolic Function ∫(sinh(x) + cosh (x))^2

A: Given- ∫sinhx+coshx2dx To find- The value of the integral. Identity Used- The above integral can be…

Q: Using integration by parts, evaluate x³ In 5x dx

A: Solution

Q: Fintsh Line

A: At a certain moment, a race official is watching a race care approach the finish line along a…

Q: sin ( Int) Let h(x)= dt. Determine the value of h(a).

A:

Q: Using Simpson's th rule evaluate 8 dx by dividing therange into equal 1+x parts.

A:

Q: refertoihe Furction (f. thXX f(x)%=X+10 D=DX hox-2xt7 Dox²+3X+n x2+3X+17 Oe-X2-x+3 40-X2-X十9 2.

A:

Q: *definite integral from bounds 0 (lower) to pi/2 (upper)* 30cos5(x)dx

A: I solve the above integral using substitution and trigonometric identities.

Q: Integration of sin^2 x?

A: Cos(2x) = 1 - 2Sin2(x)  Sin2(x)=1 - Cos(2x)2   Integration of cos(x) is Sin(x)

Q: denivative 12t'de tanx

A:

Q: Definition used- Integration by part - x* sinx dx

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: ar approximation or differential to approximate the value of 10 using the fact

A:

Q: Area under the curve y = 4 - x2  from x=-3 to x=3

A: Please see the answer bellow.

Q: ntegral of sec2x+tan2x dx

A:

Q: 5. x' sin xdx

A:

Q: integral.

A: Given: ∫sec 22w tan 22w dw To find: The best choice of u. Then find du And rewrite the given…

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A:

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A: We have to find the Riemann sum for ∫232xdx with n=3 rectangles, using left endpoints.

Q: | cos³5xsin17xdx

A:

Q: caluate integra X- Sin

A: Given : The integral is ∫ x sin ( 2x2 )dx .

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A: We have to approximate the integral using trapezoidal rule.

Q: Using Monte Carlo, estimate the value of eTy dx dy.

A:

Q: sinh x + 10 cosh x + V100 dx. e2x Evaluate 100 + sinh x

A:

Q: 4. у"- Зу' + 2у cos e*

A:

Q: sinh x + ex cosh x + ex In the indefinite Integral in(cosh x + ex)- A In(cosh x + e*) B sinh x + ex…

A: To find integrand the steps are as follows.

Q: g(x) = |sin x| ,[-n,n

A:

Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.

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A:

Q: Limit 0to2 integral√4_x^2 dx

A: To evaluate: ∫024-x2dx Solution: We know that, ∫a2-x2dx=12xa2-x2+a22sin-1xa+C Using the above…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.