Question 7 Consider the integral: 1 x²+x-6 - dx To 4 decimal places with: a) Evaluate the integral by the rectangular (mid-point) rule with 4 and 8 strips, b) Evaluate the integral by the trapezoidal rule with 4 and 8 strips, c) Evaluate the integral by the Simpson's rule with 4 and 8 strips, d) Evaluate the explicit integration, and compare the percentage errors from the three methods.

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Q: Find u from the differential equation and initial condition. du dt _____ el.8t-2.3u, u (0) = 3.7.

A: dudt=e1.8t-2.3u   given  u(0)=3.7

Q: 12. fx²e-x dx 13. fx√x² - 4 dx 14. cos √t dt

A: The given integrals are;  13) x sqrt(x2-4) 14) cos[sqrt(t)].

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A: According to question,Given equation,11-x = ∑n=0∞xn            for x<1

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A: Solution: C = 2πr & SA = 4πr2 = C2/π. i.e. surface area as a function of the circumference is…

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A: Here we have to observe the graph.

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A: Given integral:- ∫x2+5x2+1x-9x-8dx

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Q: Question 5 of 5 Solve the compound ineq -4x<=-28

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A: Given :F=&lt;3y, -5x&gt;

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Q: 37 4 S 7 9 cot8 0 csc²0 de

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A: A student drops a pen from a classroom window on the fifth floor of the  mathematics building. If…

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Q: Graph the function f(x) are -2, 0, and 1. -3 -2 -1 = 10+ 9 8 7 6 5 4 3 2 + --+ -2 -3 -2x² and draw…

A: Given:    fx=-2x2 when x=-2     f-2=-2-22               =-8 when x=0     f0=-20=0 when x=1…

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Q: Find the area enclosed by the curve x = t² - 2t y = √t and the Y axis.

A: Eliminate the parameter t and draw the graph then find the definite integration to get the area.

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Q: QUESTION 6 Use any method to evaluate the integral. 6 cm³ x dx tan x S O-2 csc4 x+C csc4 x cotx + C…

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Q: Find and classify all critical points of f (x, y) = ax^n + by^n where ab cannot equal 0 and n ≥ 2

A: Given function is f(x,y)=axn+byn,  a,b≠0 and n≥2