1. Evaluate the following integrals: (a) [₁ | (b) x³√x² + 1 dx (use simplify command to simplify your answer) | ² - 5a| dx
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solve using PYTHON/matlab
![1. Evaluate the following integrals:
(a) [a³√æ²+1 da (use simplify command to simplify your answer)
3
(b)
Lle
-2
|x² – 5x dx
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- 3- Simplify the following equation: f(4, B,C,D) = E(0,3,4,6,10,11,14,15) dm(2,7,8,12) where dm is denoted for don't care.Simplify B (x, y, z) = X’Z+X’Y+YZx+25 - Calculate the second derivative of f (x) 4.8 and h-0.4, at X - using centered divided difference and Richardson extrapolation. hi f"(x) using h) f"(x) using h2 f"(x) using Richardson extrapolation
- 1. Write a program to calculate sin and cos and determine the forward dif- ferentiation. 2. Do the same, but use central difference. 3. Plot all derivatives and compare with the analytical derivative.(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.Eliminate useless variables and symbols. Afterwards, convert to Chomsky Normal Form. (Start variable S) S -> ABBC | BA A-> abB | aa B -> bB | Aa C -> Cb | aC
- Question Number Four: Answer each one of the following questions in the space assigned: 1- Simplify each of the following expressions using boolean algebra identities: [4 Marks] a- AB + A( CD + CD') b- ( BC' + A'D) ( AB' + CD') 2- Optimize (simplify) the following boolean function F together with the don't care conditions d in Product-of-sums using k-map: F(A,B.C.D) = IIM (1,3,4,6,9,11)+Ed (0,2,5,8,10,12,14)Express the following function as a sum of minterms and as a product of max terms: F(A, B,C, D) = B'D + A'D + BDAnswer all parts from b to f
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