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# Name___________________________________ Math 2414 / Calculus II Quiz 4 / Chapter 5 Section 6 Class Time: _________________________ Use the...

Please answer the 3 files attached. I have solved them and I want to confirm my work.

Name___________________________________ Quiz 4 / Chapter 5 Section 6 Use the substitution formula to evaluate the integral. 1) 1 0 4 r dr 4 + 2r 2 2) 4 1 9 - x x dx 3) π 0 (1 + cos 5t) 2 sin 5t dt 4) 3π/4 π/4 3 + cot θ csc 2 θ dθ Find the area of the shaded region. 5) f(x) = x 3 + x 2 - 6x x -5 -4 -3 -2 -1 1 2 3 4 5 y 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 (-4, -24) (0, 0) (3, 18) x -5 -4 -3 -2 -1 1 2 3 4 5 y 30 25 20 15 10 5 -5 -10 -15 -20 -25 -30 (-4, -24) (0, 0) (3, 18) g(x) = 6x 6) y = x 2 - 4x + 3 x -3 -2 -1 1 2 3 4 5 y 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 x -3 -2 -1 1 2 3 4 5 y 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = x - 1 1
7) y = 2x 2 + x - 6 y = x 2 - 4 x -4 -3 -2 -1 1 2 3 4 y 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 x -4 -3 -2 -1 1 2 3 4 y 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 8) y = x 4 - 32 x -5 -4 -3 -2 -1 1 2 3 4 5 y 5 -5 -10 -15 -20 -25 -30 -35 -40 x -5 -4 -3 -2 -1 1 2 3 4 5 y 5 -5 -10 -15 -20 -25 -30 -35 -40 y = - x 4 9) x - p - p 2 p 2 p y 2 1 -1 -2 x - p - p 2 p 2 p y 2 1 -1 -2 y = - cos x y = cos 2 x Find the area enclosed by the given curves. 10) y = 2x - x 2 , y = 2x - 4 11) y = x, y = x 2 12) y = - 4sin x, y = sin 2x, 0 x π 13) y = csc 2 x, y = cot 2 x, x = π 4 , and x = 4 2
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