(Solved): 61, 63, and 64 pls and explain  In Problems 61-67, use an area formula from geometry to find th ...

In Problems 61-67, use an area formula from geometry to find the value of each integral by interpreting it as the (signed) area under the graph of an appropriately chosen function. 61. \( \int_{-2}^{3}|x| d x \) 62. \( \int_{-3}^{3} \sqrt{9-x^{2}} d x \) 63. \( \int_{2}^{5}\left(\frac{1}{2} x-4\right) d x \) 64. \( \int_{1 / 2}^{1} \sqrt{1-x^{2}} d x \) 65. \( \int_{-2}^{2}\left(\sqrt{4-x^{2}}-2\right) d x \) 66. \( \int_{0}^{1} \sqrt{2-x^{2}} d x \) 67. \( \int_{-3}^{0}\left(4-\sqrt{9-x^{2}}\right) d x \)