Calculate the area under the curve y= 3x +3 for values between [1, 4].
A)15.75
B)157.5
C)993.25
D)10.5
E)31.5

Question

Quizplus · Accepted Answer

The area under the curve can be calculated using the definite integral of the function from the lower to the upper limit. For the function y = 3x + 3, the integral from 1 to 4 is:∫(3x + 3) dx from 1 to 4 = (3/2)x^2 + 3x evaluated from 1 to 4= [(3/2)(4)^2 + 3(4)] - [(3/2)(1)^2 + 3(1)]= [(3/2)(16) + 12] - [(3/2)(1) + 3]= [24 + 12] - [1.5 + 3]= 36 - 4.5= 31.5

Calculate the Area Under the Curve Y= 3x +3 for Values