Question

In the following exercises, evaluate the integral using area formulas. 3 76. int_0^3 (3 - x)dx 3 77. int_2^3 (3 - x)dx 3 78. int_{-3}^3 (3 - |x|)dx 6 79. int_0^6 (3 - |x - 3|)dx 2 80. int_{-2}^2 sqrt{4 - x^2}dx 5 81. int_1^5 sqrt{4 - (x - 3)^2}dx 12 82. int_0^{12} sqrt{36 - (x - 6)^2}dx

          In the following exercises, evaluate the integral using area formulas.
3
76. int_0^3 (3 - x)dx
3
77. int_2^3 (3 - x)dx
3
78. int_{-3}^3 (3 - |x|)dx
6
79. int_0^6 (3 - |x - 3|)dx
2
80. int_{-2}^2 sqrt{4 - x^2}dx
5
81. int_1^5 sqrt{4 - (x - 3)^2}dx
12
82. int_0^{12} sqrt{36 - (x - 6)^2}dx

In the following exercises, evaluate the integral using area formulas.
3
76. int0^3 (3 - x)dx
3
77. int2^3 (3 - x)dx
3
78. int-3^3 (3 - |x|)dx
6
79. int0^6 (3 - |x - 3|)dx
2
80. int-2^2 sqrt4 - x^2dx
5
81. int1^5 sqrt4 - (x - 3)^2dx
12
82. int0^12 sqrt36 - (x - 6)^2dx

Added by Jeffery M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kathleen Carty

10/12/2024

Step 1

- The function \(3-x\) is a linear function, forming a right triangle with the x-axis from \(x=0\) to \(x=3\). - The base of the triangle is 3, and the height is 3 (since \(3-0=3\)). Show more…

Show all steps

Thanks for your feedback!

In the following exercises, evaluate the integral using area formulas. 76. ∫_0^3 (3-x)dx 77. ∫_2^3 (3-x)dx 78. ∫_(-3)^3 (3-|x|)dx 79. ∫_0^6 (3-|x-3|)dx 80. ∫_(-2)^2 √(4-x^2)dx 81. ∫_1^5 √(4-(x-3)^2)dx 82. ∫_0^12 √(36-(x-6)^2)dx