2. Evaluate the definite integrals. (b) Cos (x²) dx リ2

Q: Evaluate the integral. |sin° (x)cos“ (x)dx

A: In this question, the exponent of cos(x) is even i.e. 4, and the exponent of sin(x) is odd i.e 5,…

Q: In the given equation as follows , find the indefinite integral using the substitution x =5 sec θ.…

A: In some cases integral can be simplified to standard integrals by an appropriate substitution. For…

Q: 10 dx

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Q: 1 2 -5) dx x3

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Q: Use the Exponential Rule to find the indefinite integral. (Use C for the constant of / 9xe®x? dx

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Q: In the given equation as follows , use a table of integrals to evaluate the definite integral :-…

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: -aluate the definite integral (Show your ork). + sin(x) + 1 )dx

A: Using integration ,

Q: dy =

A:

Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: \ rV 25 – x2 Evaluate the indefinite integral. dx -

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Q: Find the indefinite integral using the substitution x = 4 sin 0. (Remember to use absolute values…

A: To find: Integration

Q: y=sin

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Q: Find the indefinite integral using the substitution x = 8 sin(@). (Use C for the constant of…

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Q: In the given equation as follows , find the indefinite integral using the substitution x =5 sec θ.…

A: In some cases an integral can be converted to a standard integral with an appropriate substitution.…

Q: Evaluate the indefinite integral given below. 2e3 sin (4z) cos (4x) dx Provide your answer below:…

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Q: Use a change of variables or the table to evaluate the following indefinite integral. dx e ex +5…

A: We have to find the integral

Q: In the following equation/s, find the indefinite integral :-   see the equation attached here

A: Given integral: ∫5+4x22dx We know that a+b2=a2+2ab+b2 ∫5+4x22dx=∫25+40x2+16x4dx

Q: Find the indefinite integral. sinh(2 – 7x) dx Step 1 First, let u = 2 - x. Now, differentiate u with…

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Q: Evaluate the definite integral. 1 Г хзе-ха dx 0 Need Help? PRENT

A: The given definite integral is ∫01x3e-x4dx. Evaluate the integral value. Here we use the integration…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | 2 sect() dx

A: Note : As per our guidelines we are supposed to answer only one question . Kindly repost other…

Q: | 5 cos(x²) dæ a) Approximate the definite integral with the Trapezoid Rule and n = 6. b)…

A: (a)Trapezoidal Rule ∫abf(x) dx=∆x2(f(x0)+2f(x1)+2f(x2) + ... +2f(xn-1)+f(xn))where ∆x=b-anConsider…

Q: 42. y=+on [1/2,2] 6

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Q: Evaluate the integral (1+lnx)5/ x dx from 1 to e.    Find the indefinite integral: sin(x)…

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Q: Use a suitable substitution to find the indefinite integral S csc(sin 0) · cos(0)d0

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Q: Find the following integral. Note that you can check your answer by differentiation. dx = 5+ e5z

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Q: In the given equation as follows , use a table of integrals to find the indefinite integral:-   See…

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Q: Evaluate the definite integral. sec (x/4) dx 0.

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Q: Inx dx where x>0. 1

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Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx 6 + cos x Need Help?…

A: Let's find.

Q: In the given equation as follows , find the indefinite integral using the substitution x =5 sec θ.…

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: Please calculate the following definite integral and express your final result using parameter a e"…

A: We have, I=∫01exsinaxdx On using the integration by parts, we get the result as I=∫exsinax…

Q: h sin 2 xdx X COs 2

A:

Q: Use the Change of Variables Formula to evaluate the definite integral. dx (x? +2) (Use symbolic…

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Q: Given the integral 6x + 9 dx 2 Use the integral table to help you find the Anti Derivative of the…

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Q: (a) Evaluate the following integrals by interpreting each in terms of areas and using basic…

A: As per our guidelines, we are allowed to answer only one question. Since, you have posted multiple…

Q: Given 4 cos(x²) dx 2 How many Trapezoids will you need to estimate the definite integral to an…

A: Given the integral I=∫24cosx2dx. (a) We need an accuracy of 0.001 when the Trapezoidal rule. The…

Q: valuate the indefinite integral. (Use C for the consta | (In(x))14 dx

A: Given: ∫lnx14xdx

Q: Use a change of variables or the table to evaluate the following definite integral. 15 e 3x dx

A: Given integral is ∫0315e3xdx Substitute 3x=y ⇒3dx=dy⇒dx=dy3 And limit of integration will be change…

Q: f(x)=√ √atan(x) dx f(x)= | sinh xã dx

A: Two functions are given by, fx = ∫atanx dx and fx = ∫sinh x2 dx. The objective is to find the…

Q: Find the indefinite integral. Remember to include a "+ C" if appropriate. sin (a) (204 8x dx = 8.

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Q: 22. Given that sinh 2 =, the value of cosh z is A. +- В. D. 4

A: Given: sinh x=34

Q: e4x dx 6+ e4x

A: Given: I=∫e4x6+e4xdx

Q: Find the exact value of the integral using formulas from geor 5. (2+2x)dx 2. |(2 + 2x)dx = (Simplify…

A: Given: ∫25(2+2x)dx To find the exact value of the integral using geometry

Q: 2 Find the definite integral o tan(x)dx using strips of width for the trapezium rule correct to…

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Q: 2. Find the following definite and indefinite integrals. Use Substitution when needed a) f…

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Q: (-5sin t) dt

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Q: Find the definite integral 10 (2х — 3) dx

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Q: You plan to approximate the definite integral, 10 (8x + 3)?dx using both a left and right sum. Which…

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Q: valuate the indefinite integral. ∫9sin^5(x)cos(x)dx

A: Given that the integral we need to evaluate that  integral. let I=∫9sin^5(x)cos(x)dx let us…

Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ

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.