Q2/ Use Composite Simpson integral formula to find the value of the following integral. 10 1 Į dx, consider n = 10 1+x² 0 Q3/ Using modified Euler's method, determine the value of y when x = 0.2 given That dy =x+ √y, y(0) = 1, Take h = 0.2 dx

Q: Evaluate the following integrals. a. Lx-x* + 3 dx Se cos(x) esin x dt T/2 ъ.

A: Both the answers can be solved as below

Q: 1 J = [ exp(-x²)dx Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1 Evaluate J by…

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Q: Evaluate the definite integral. 1 #111: e3/x dx а. xe dx b. #113: 0. 1

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Q: x1/2 dx x3/4 + 1 Let x = z8 dx = 8z7dz Is the substitution the most appropriate one? Explain your…

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Q: Two ways Evaluate the following integrals two ways.a. Simplify the integrand first and then…

A: Given, an integration ,

Q: 1/2 2. Approximate the integral: 1 - cos(2x) dx within an error of 0.01. x2

A: According to question given that∫0121-cos2xx2dx within an error of 0.01

Q: Given the following integral dx Use your knowledge about the Substitution Method to find (1) "u",…

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Q: Find the indefinite integral. (Use C for the constant of integration.) coss t dt sin t

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Q: Evaluate the following indefinite integral Use C for any constant of integration 81 – x10 dx =

A: ∫tn dt = tn+1n+1+C ∫cos(at) dt =1asin(at)+C

Q: Evaluate the following integrals. Give exact values for your answers. Explain the motivation for…

A: (a).  The integral is: I=∫x4+x223 dx

Q: Use integration by parts to evaluate the definite integral. 8t? In(t)dt Give an exact answer

A: ∫1e8t2lntdt=8·∫1et2lntdt=813t3lnt-3·∫t23dt1e=813t3lnt-3·t391e=813t3lnt-t331e=82e39+19=82e3+19

Q: 11x dx Since this function does not have an elementary antiderivative, use integration by parts to…

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Q: 1. Evaluate the integral by reversing the order of integration 3 L Lea dx dy.

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Q: Which value has the following integral I r(2) 2.6 So 2 -2.6a dx e a. 3.3800 b. 0.4438 c. 0.7692 d.…

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Q: Question 2: Use the Trapezoid rule to evaluate the following definite integral: | dx using n=4 as…

A: The Trapezoidal Rule: Assume that f(x) is continuous over [a,b] and be the positive integer and…