Chapter 4.5, Problem 77E

(a)

To determine

To calculate: Using ${\displaystyle {\int }_0^6{x}^2}dx=72$ the value of definite integral ${\displaystyle {\int }_{-6}^6{x}^2}dx$ using Fundamental theorem of calculus.

(b)

To determine

To calculate: Using ${\displaystyle {\int }_0^6{x}^2}dx=72$ the value of definite integral ${\displaystyle {\int }_{-6}^0{x}^2}dx$ using Fundamental theorem of calculus.

(c)

To determine

To calculate: Using ${\displaystyle {\int }_0^6{x}^2}dx=72$ the value of definite integral ${\displaystyle {\int }_0^6-2x^2}dx$ using Fundamental theorem of calculus.

(d)

To determine

To calculate: Using ${\displaystyle {\int }_0^6{x}^2}dx=72$ the value of definite integral ${\displaystyle {\int }_{-6}^{6}3x^2}dx$ using Fundamental theorem of calculus.