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Main points of this exam paper are: Find Displacement, Evaluate Following Integrals, Riemann Sum, Midpoint Rule, Total Distance Traveled, Real Number, Parametric Equations, Parallel to Vector, Equations of Line, Equation of Plane
Typology: Exams
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Student signature: Show all your work and give reasons for your answers. Good luck! Part I Each problem in part I is worth 5 points; Show your work!!
Evaluate the following integrals
(1)
0 x
(^3) ex^4 +3 (^) dx
1
sin^2 (x) dx
x sin(x) dx
∫ (^) x (x−2)^2 dx
(9) If F (x) =
x e
t^2 dt find F ′(x).
(10) Approximate
0 e
x^2 dx using a Riemann sum with 3 terms and the midpoint rule.
Part II Credit for each problem as indicated. Justify all your work for full credit!!
Evaluate the following integrals.
15 pts.
0 arctan(x)^ dx
15 pts. Find the displacement and the total distance traveled of a particle whose velocity is given by v(t) = t^2 − 1 for − 1 ≤ t ≤ 2.
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