Integration and Accumulation of Change

Differential equation

Solution equation

Value theorem

$6x^2 + 12x + 8$

$4x^3 + 8x^2 +16x$

$4x^2 + 8x + 16$

$6x^3 -12$

Multiplying by $\frac{1}{5}$ outside and inside of the integral

Applying partial fraction decomposition

Using substitution with u-substitution where $u = e^{5t}$

Implementing integration by parts with $dv = e^{5t} dt$

Constant

None of the above

Increasing

Decreasing

The average value of the function over a given interval

The accumulation of change in the function over a given interval

The maximum value of the function over a given interval

The rate of change of the function at a specific point

When t = -4 seconds

When t = 4 seconds

When t = -2 seconds

Never; acceleration isn't zero at any time

The maximum rate of change

The accumulation of change

The average rate of change

The instantaneous rate of change

It's differentiable everywhere even though it's not continuous at t=1.

It's continuous everywhere except at t=1 where it's not differentiable either.

It's neither continuous nor differentiable anywhere because it has a rational expression with variable in the denominator.

It’s discontinuous only where its derivative does not exist.

The definite integral is equal to the average rate of change of the function over the interval.

The definite integral is equal to the maximum rate of change of the function over the interval.

The definite integral is equal to the derivative of the function evaluated at b minus the derivative of the function evaluated at a.

The definite integral is equal to the function evaluated at b minus the function evaluated at a.

The definite integral depends on the value of the constant.

The definite integral is always positive.

The definite integral is always zero.

The definite integral is always negative.