Question

Determine whether the integral is convergent or divergent. 0 1 5 − 6x dx −[infinity].

A. Convergent
B. Divergent
C. It depends on the upper limit of integration
D. It depends on the lower limit of integration

Answer 1

The integral is convergent.

Step-by-step explanation:

To determine whether the integral is convergent or divergent, we need to evaluate each part of the integral separately. The given integral is from 0 to 1, and then from 5 to -6x. Let's break it down:

1. The integral from negative infinity to zero is 0, because the integrand is negative infinity there.
2. The integral from zero to 1 can be calculated by finding the antiderivative of -6x, which is -3x^2. Evaluating it from 0 to 1, we get -3.
3. The integral from 1 to 5 can be calculated similarly, and it also gives us -3.
4. The integral from 5 to infinity is 0, because the integrand is negative infinity again.

Adding up all the parts, we have 0 + (-3) + (-3) + 0 = -6. Since the integral is a finite value, it is convergent.