What is the definite integral of:

Evaluate the exponential function below from x = 1 up to x = 5.

Evaluate the function below from x = 1 up to x = 3.

All associated angles are in radians.

Suppose that a tumor in a person's body is spherical in shape. If, when the radius of the tumor is 0.5 cm, the radius is increasing at the rate of 0.001 cm per day, what is the rate of increase of the volume of the tumor at that time?

Which of the following is the general solution of:

Evaluate the first derivative of the function below at (2, 2).

The associated angles are in radians.

Evaluate the radical function below from t = 2 up to t = 3.

Find the area underneath the curve. Express your answer into 2 decimal places. 

Evaluate:

Evaluate the function below from x = 1 up to x = 4.