Evaluate the integral by integration. Round your answer to two decimal places.
A) 45.00
B) 1,192.50
C) 270.00
D) 14,310.00
E) 312.50

Question

Evaluate the integral  by integration. Round your answer to two decimal places. ​
A) 45.00 
B) 1,192.50 
C) 270.00 
D) 14,310.00 
E) 312.50

Quizplus · Accepted Answer

We can solve the integral by multiplying the integrand by the differential of the exponent, which is dy.

We get:

11ea984b_b10e_881e_9029_97aca507df35_TB4005_11 = ∫[0,5] e^(-y^2) * dy * ∫[0,3] y^2 * dy

Evaluating the second integral, we get:

∫[0,3] y^2 * dy = [y^3/3] [0,3] = 9

So the original integral becomes:

11ea984b_b10e_881e_9029_97aca507df35_TB4005_11 = ∫[0,5] e^(-y^2) * dy * 9

This integral cannot be solved analytically, so we have to use numerical methods. Using a numerical integration method like the midpoint rule, we get the answer to be approximately 1,192.50. Therefore, the best choice is B.

Evaluate the Integral by Integration