Evaluate the following integrals: (a) J (t2+5t -1)6(t)dt (b) fix(t2 + 5t-1)δ(t)dt t) is a inction.
9. (a) Let Ao(x) = / (1-t*)dt, Ai(z) = / (1-t2) dt, and A2(z) = / (1-t2)dt. Compute these explicitly in terms ofェusing Part 2 of the Fundamental Theorem of Calculus. b) Over the interval [0,2], use your answers in part (a) to sketch the graphs of y Ao(x), y A1(x), and y A2(x) on the same set of axes. (c) How are the three graphs in part (a) related to each other? In particular, what does Part 1 of...
Evaluate the integral. 2 1 t3 t2 − 1 dt √2 Part 1 of 7 Since 2 1 t3 t2 − 1 dt √2 contains the expression t2 − 1, we will make the substitution t = sec θ. With this, we getdt = $$sec(θ)tan(θ) dθ. Part 2 of 7 Using t = sec θ, we can also say that t2 − 1 = sec2θ − 21 1 = tan θ. Part 3 of 7 Using t =...
(1 point) Use Part I of the Fundamental Theorem of Calculus to find the derivative of cos(t2+t)dt n'(z) = (1 point) Use Part I of the Fundamental Theorem of Calculus to find the derivative of cos(t2+t)dt n'(z) =
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
Calculate v(t) and a of Functions Graph using Matlab xe), vC), a(t) 2ttt cox 2. lOt"-4t+2¢? t2(10t4t t3 1 +0 -t dt 1e -t Calculate v(t) and a of Functions Graph using Matlab xe), vC), a(t) 2ttt cox 2. lOt"-4t+2¢? t2(10t4t t3 1 +0 -t dt 1e -t
(1 point) Consider the function f(x) = f* cos(t) – 1 dt. t2 Which of the following is the Taylor Series for f(x) centred at x = 0? w A. (-1)" (2n – 1)(2n)! -x2n- +C. n=0 (-1)"(2n – 2) 2n–3. B. (2n)! n=1 c. Σ (-1)" (2n + 1)! -x2n-2 n=1 D. Š (-1)" -X2n-1 (2n – 1)(2n)! n=1
(1 point) Consider the function f(x) = Es cos(t) – 1 t2 dt. Which of the following is the Taylor Series for f(x) centred at x = 0? 2n-1 Α.Σ (-1)" (2n – 1)(2n)! X +C. n=0 oo 2n-1 B. (-1)" (2n – 1)(2n)!" X n=1 (-1)" X20-2 (2n + 1)! M n=1 D. iM: (-1)"(2n – 2), 2n–3 (2n)! X n=1
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.
Q9 (Approximation of π) (a) Show that 1/1 + t2 = 1 − t2 + t4 − ... + (−1)n−1 t 2n−2 + (−1)n t2n /1 + t2 for all t ∈ R and n ∈ N. (b) Integrate both side in (a), show that tan−1 (x) = x − x3/3 + x5 /5 − ... + (−1)n−1x 2n−1/ 2n − 1 + Z x 0 (−1)n t2n /1 + t2 dt. (c) Show that tan−1 (x) − ( x...