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61.

Find the area of the region {(x, y): x² + y² ≤ 1 ≤ x + y}.

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62.

Find the area of the region bounded by the circle x² + y² = 1 and x + y = 1. Also draw a rough sketch.

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63.

Find the area of the region {(x, y): x² ≤ y ≤ |x|}.
Or
Find the area of the region bounded by the parabola y = x² and y = |x|.

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64. Draw the rough sketch and find the area of the region:
{(x, y) : y² ≤ 8 x, x² + x² ≤ 9}

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65. Find the area of the region {(x, y): y² ≤ 4 x, 4x² + 4 y² ≤ 9}

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66. Find the area lying above x-axis and included between the circle x² + y² = 8 x and inside of the parabola y² = 4 x.

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67. Calculate the area enclosed in the region:

open curly brackets left parenthesis straight x comma space straight y right parenthesis space semicolon space space straight x squared plus straight y squared space less or equal than space 1 space less than space straight x plus 1 half straight y close curly brackets

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68. Find the area of the circle x² + y² = 16 which is exterior to the parabola y² = 6x.

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69. Find the area of the circle 4x² + 4y² = 9 which is interior to the parabola y²= 4 x.

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70. Draw a rough sketch of the region {(x, y): y² ≤ 5 x, 5 x² + 5 y² ≤ 36} and find the area enclosed by the region using method of integration.

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