Evaluate the integral by integration. Round your answer to two decimal places.

Question

Evaluate the integral  by integration. Round your answer to two decimal places. ​

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