Find the area of the region under the given curve over the indicated interval.
A)10 sq units
B)12 sq units
C)9 sq units
D)6 sq units

Question

Find the area of the region under the given curve  over the indicated interval. 
A)10 sq units 
B)12 sq units 
C)9 sq units 
D)6 sq units

Quizplus · Accepted Answer

To find the area under the curve, we need to integrate the function over the given interval. 
∫(11x-x²)dx from x=1 to x=2
= [(11/2)x² - (1/3)x³] from x=1 to x=2
= [(11/2)(2²) - (1/3)(2³)] - [(11/2)(1²) - (1/3)(1³)]
= (22/2 - 8/3) - (11/2 - 1/3)
= 9/2 - 17/6
= 27/6 - 17/6
= 10/6
= 5/3
Therefore, the area is 5/3 square units, which is closest to 9 square units, making choice C the best answer.

Find the Area of the Region Under the Given Curve