Find the area of the shaded region for the function .

Question

Find the area of the shaded region for the function  . ​  ​

Quizplus · Accepted Answer

To find the area of the shaded region, we need to find the definite integral of the function between the limits 0 and 4.

∫[0,4] (4x - x^2) dx

= [(2x^2 - x^3)/3] from 0 to 4

= (2(4)^2 - (4)^3)/3 - (2(0)^2 - (0)^3)/3

= (32 - 64)/3

= -32/3

However, the area can only be positive, so we take the absolute value, which is 32/3.

The answer that matches this value is option C: 11eac44f_ecee_938a_bedf_4bdd3f7739e4_TB7497_11.

Find the Area of the Shaded Region for the Function