2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx 1+x³ b) Estimate the minimum number of subintervals needed to approximate the

Q: i) ii) The following two functions are given: y = x and y = x¹. Sketch the two curves on the same…

A: Topic = Application of integration

Q: Use the Trapezoidal Rule and Simpson's Rule with four subintervals to estimate x* dx.

A: Trapezoidal Rule

Q: The base of a tank is a circle, represented by x2 + y2 = 4 (in feet). The side of the tank is…

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Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

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Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: b. Approximate the area bounded by f(x)=x² - 2x+6 on the x-interval [0,3] usingn = 3 rectangles and…

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Q: Find the volume of a right circular cone with base radius r unites and height h units using the…

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Q: Q1) Consider the function /(x) = x2 + 2 in the interval (0, 2). Approximate the area under the curve…

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Q: Use Simpson's rule with n = 6 to estimate the curved surface area when the parabol y = 2x² on the…

A: Given: The equation of parabola is: y=2x2. To Do: Using Simpson's rule with n=6 on the interval 0, 3…

Q: c) Consider the following two functions are given: y = 2x - x² and y = x². i. Sketch the two curves…

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Q: Use Trapezoidal and Simpsons 1/3 rule to estimate integral ( - 2x° + 7x - 5) de.

A: The expression ∫13x3-2x2+7x-5dx. We have to use Trapezoidal and Simpsons 13 rule to estimate the…

Q: (A) Suppose R is the region in the second quadrant bounded by the circle x² + y² = 4, the lines y =…

A: Solve the following, Suppose R is the region in the second quadrant bounded by the circle x2+y2=4,…

Q: )Find the volume of the solid obtained by rotating the sine function between x 0 and x t about the…

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Q: 3.) Determine the absolute and relative error that occurs when approximating the integral 32x² dx…

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Let Fes) = fcx-s)dx Find fes) for %3D fex).x^, a constant the funchion where n is

A: Definite integral of the function ∫abf(x)=F(b)-F(a) where F is antiderivative of f .