Hello course team, I need help formulating the following calculus two problems. Please show work and explanation.

Please be precise and accurate.

Integrals Problem # 1 (16 points) Use the definition of improper integral to evaluate the following integral (be attentive with the signs, use limit for explanation) x . e-2x' dx = -00 Problem # 2 (16 points) Evaluate (clearly state substitution and keep the exact answer with radical signs) x2x3 + 4 dx = Problem # 3 (12 points) Use integration by parts to evaluate. Clearly state u =. ., du =..., v =..., du =..., x2 . In(2x) dxProblem # 4 (12 points) Use partial fraction decomposition to evaluate and show the procedure of finding coefficients J' Tk p x2+3x70"" Problem # 5 (16 points) Use Trigonometric Substitution (fully complete the problem by applying \"right triangle\" if applicable) x2 dx f\\M o Problem # 6 (12 points) Evaluate the following Trigonometric integral T f:-: L V2L - e 0 Sequences and Series Problem # 7 (12 points) E3 /1 Find limit of the terms of the sequence {(1 + ?2:) } Do not just use formula, apply LH Rule State whether sequence converges or diverges. Problem # 8 (16 points) Use the Limit Comparison Test to determine whether the given series converge or diverge: clearly state b, Jjustify why ). b,, diverges or converges L noo n clearly state your conclusion oo Vn -5 Z VIR ) n=10 Problem # 9 (12 points) Determine whether the given series Converge Absolutely, Converge Conditionally, or Diverge. Give reasons for your conclusion: state the test(s) name(s) and clearly show the procedure. S 5 ;(1)"\" Problem 10 (12 points) (a) find all values of x for which each given power series converges (b) check both end points (if any) (c) state the interval of convergence for the series in interval notation (x + 2)n n22n n=1 Problem # 11 (12 points) Calculate the Taylor polynomial P2 for the given function centered at the given value of C (state three nonzero terms). Be attentive that c=9 1 f ( x) = C =9 xApplication problems (3 problems) Problem # 12 (12 points) The velocity of a car after seconds is (30 5t) feet per second. (a) How many seconds does it take for the car to come to a stop (v=0)? (b) How far does the car travel while coming to a stop? Problem # 13 (12 points) Find area between two curves y; = 4x + 16 and y, = 2x% + 10 Problem # 14 (23 points) Let R be the region bounded by the following curves (in the 1% Quadrant) y=6Vx, y=2x R is revolved about the x axis. Set up and evaluate an integral that gives the Volume of the solid