Resuelto 30. Region between y=x and x+y=8 over [2,3] In

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Pregunta: 30. Region between y=x and x+y=8 over [2,3] In Exercises 31-50, sketch the region enclosed by the curves and compute its area as an integral along the x-or y-axis. 31. y=25−x2,y=x2−25 32. y=x2−6,y=6−x3,x=0 33. x+y=4,x−y=0,y+3x=4 34. y=8−3x,y=6−x,y=2 35. y=15−x,y=2x,x=0 36. y=x2+1x,y=5x 37. x=∣y∣,x=1−∣y∣ 38. y=∣x∣,y=2x+3 39. x=y3−18y,y+2x=0 40.
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Paso 1
QUSETION-39

The region is bounded by the curves are

$x = y^{3} - 18 y$
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Texto de la transcripción de la imagen:

30. Region between

y = x

and

x + y = 8

over

[2, 3]

In Exercises 31-50, sketch the region enclosed by the curves and compute its area as an integral along the

x

-or

y

-axis. 31.

y = 25 - x^{2}, y = x^{2} - 25

32.

y = x^{2} - 6, y = 6 - x^{3}, x = 0

33.

x + y = 4, x - y = 0, y + 3 x = 4

34.

y = 8 - 3 x, y = 6 - x, y = 2

35.

y = 15 - x, y = 2 x, x = 0

36.

y = \frac{x}{x ^{2} + 1}, y = \frac{x}{5}

37.

x = ∣ y ∣, x = 1 - ∣ y ∣

38.

y = ∣ x ∣, y = \frac{x}{2} + 3

39.

x = y^{3} - 18 y, y + 2 x = 0

40.

y = x x - 2, y = - x x - 2, x = 4

41.

x = 2 y, x + 1 = (y - 1)^{2}

42.

x + y = 1, x^{1/2} + y^{1/2} = 1

43.

y = cos x, y = cos 2 x, x = 0, x = \frac{2 π}{3}

44.

y = tan x, y = - tan x, x = \frac{π}{4}

45.

y = sin x, y = csc^{2} x, x = \frac{π}{4}

46.

x = sin y, x = \frac{2}{π} y

47.

y = e^{x}, y = e^{- x}, y = 2

48.

y = 5 e^{x}, y = e^{2 x}, x = 0

49.

y = \frac{l n x}{x}, y = 0, x = e

50.

y = \frac{l n x}{x}, y = \frac{( l n x ) ^{2}}{x}