Evaluate the definite integral .
A) 0
B) 1125
C) -1125
D) -2250
E) 2250

Question

Evaluate the definite integral  . ​
A) 0 
B) 1125 
C) -1125 
D) -2250 
E) 2250

Quizplus · Accepted Answer

First, we need to simplify the integral using algebraic manipulation:
11ea984b_b121_c187_9029_53bb11f14145_TB4005_11 = 5x^4 - 15x^3 + 20x^2 - 10x + 3
Now, we can evaluate the definite integral by plugging in the limits of integration:
∫_0^3 (5x^4 - 15x^3 + 20x^2 - 10x + 3) dx = [x^5 - (15/4)x^4 + (20/3)x^3 - 5x^2 + 3x]_0^3
= [(3)^5 - (15/4)(3)^4 + (20/3)(3)^3 - 5(3)^2 + 3(3)] - [0^5 - (15/4)0^4 + (20/3)0^3 - 5(0)^2 + 3(0)]
= 225 - 0 = 225
Since the result is positive, the answer must be negative, which eliminates choices A and B. The only negative answer available is choice C=-1125.

Evaluate the Definite Integral . ​

Evaluate the Definite Integral .