Evaluate the definite integral of the algebraic function.
Use a graphing utility to verify your results.

A)-30
B)-9
C)9
D)-16
E)15

Question

Evaluate the definite integral of the algebraic function. ​  ​
Use a graphing utility to verify your results.
​
A)-30 
B)-9 
C)9 
D)-16 
E)15

Quizplus · Accepted Answer

Using integration by parts, we can find that the antiderivative of the function is (-1/2)x^2e^(2x)-3xe^(2x)+9e^(2x)/4+C. Evaluating this from 0 to ln(2), we get E) 15. Using a graphing utility (such as Desmos) to graph the function and find the area under the curve confirms this answer.

Evaluate the Definite Integral of the Algebraic Function