Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.
A) -516
B) 516
C) 618
D) 1185
E) -1974

Question

Evaluate the definite integral of the algebraic function.  Use a graphing utility to verify your results.
A) -516 
B) 516 
C) 618 
D) 1185 
E) -1974

Quizplus · Accepted Answer

The definite integral of the given function can be evaluated by using the power rule of integration. We have:

∫(x^3 + 2x^2 - 3x - 4)dx = (x^4/4) + (2x^3/3) - (3x^2/2) - 4x

Now, substituting the upper and lower limits of integration, we get:

[(8^4/4) + (2*8^3/3) - (3*8^2/2) - 4*8] - [(2^4/4) + (2*2^3/3) - (3*2^2/2) - 4*2]
= (4096/4 + (2*512/3) - (3*16/2) - 32) - (8/4 + (2*8/3) - (3*2/2) - 8)
= 1031.6666667 - 586.6666667
= 445

Therefore, the best choice is C, 618. A graphing utility can be used to verify the result.

Evaluate the Definite Integral of the Algebraic Function