Find the intergral St-st-tox) dx a) 2ln (x1 - 25 6 6x t6 6xxt C.) 2...
Evaluate the following integral. + 6x - 1 dx X-X Find the partial fraction decomposition of the integrand. St*6x=1&x=SO dx Evaluate the indefinite integral. S*** + 6x - 1 3 X-X dx =
Find (and prove) a general formula for the intergral a^(bx) cos(cx)dx , for any constants a,b,c
Q3. x² +6x+8y + 25 = 0 * +6x= -84–25 (x+3)²-9=-84-95 (x+3) = -84 – 16 (x+3)= -8[y + water (-3,-2) faces (-3,-4) Axis of st. x=-3 Directx y zo 1233 Arab Academy for Science, Technology and Maritime Transport - Sharjah Branch No.5: F(x) = In 1 + x Solution: F(x)= In 1+x F(0) = ln 1 = 0 F(0)=1 F"(0)=-1 F"(0) = 2 F4(0) = -6 F'(x) =x = (1+x)" F"(x) =-(1+x)=2 F"(x) = 2(1+x)=3 F4(x) = -6(1+x)-4 F(x)=F(0)...
x = -6 28. Suppose that {$(x)dx=-6. Se (x)dx = 8 and !!) . Find ļ[3/(x)+8(*)]dx (x) dx = 8 . Finds d. 6 e. None of these a. -10 b. 11 c. 18 29. If 0-1 - 51+4 represents the rectilinear motion of a particle, the particle changes direction at what time? Assume is in seconds. a. 4.5 sec b. 2 sec C. 1.5 sec d. 2.5 sec e. None of these
4. Integration: TT (a) Si Jachtvoz dx (b) sin x dx (6-cos x)3 (c) , (2-2)' (3) dx (d) St(t - 5)8dt 6x7-x*+VX-4 dx x2
1 (a) Consider the integral dx. e32 e-91 + e-6x +1 Make the substitution u = e-34 and rewrite the integral in terms of u only. DO NOT attempt to evaluate the integral. (b) Let f(x) be a function with the properties that f(0) = 1, f(2) = 2, xf(x) dx = 4 and f(x) dx = 1. / 0 Use this information to find a se xf'(2) dr.
Consider the linear system described by: 10 x1 + 9x2 +8 x3 + 8 x4100 10 x1 + 9 x2 +8x3 6 x4 70 6x, + 10x2+9x3 +8x4-50 6 x1 10 x2 +8x3 +0.01 x420 Write a Matlab script to: a) Find the solution (x) b) Find the: codon number of the sysicern c) Find the number of unreliable digits in the answer d) Find a value for b such that x3 0 (Hint: b1 decreases from 100, use increments...
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
QUESTION 25 Find an integrating factor of the form x"y" and solve the equation. (2x+y2-9y)dx+ (3y-6x) dy=0; y(1) =1 A 4x2y3 – 3x3y2 = 1 o e x?y2-3x3y2 = -2 ocx?y* - 3x^y2=-2 02.3x2y3 – x3y2=2 Ex?y-3x?y2=-2
1 of 4 he following integrals: .nx dx (parts) 4 2) [4x² In(6x) dx parts) 3) 1x*sin2x dx (parts) 4) ſcosº x dx (trig identity) 5) ſsinº x cos*x dx (trig identity) 6) ſcosº xvsin x dx (reduction) 7) ſcot* x dx reduction) 8) ſtan x secºx dx (reduction)