Final answer:
To find the area under the curve using calculus, you can calculate the area of the right triangle formed by the curve and the x-axis. The derivative of the function gives us the slope of the curve at any given point.
So, the correct answer is: a) Integral of the function.
Step-by-step explanation:
b. The area under the curve can be found by calculating the area of the right triangle formed by the curve and the x-axis. This can be done by finding the base of the triangle, which is the interval of x-values, and the height, which is the corresponding y-value of the curve. The formula for the area of a triangle is A = (base * height) / 2.
c. The derivative of the function gives us the slope of the curve at any given point. This can be helpful in understanding the changing rate or velocity of the function.
In calculus, to find the area under a curve, you typically use the definite integral of the function over a given interval. The integral represents the accumulation of infinitesimally small areas under the curve, and finding the definite integral over a specific range gives you the net area between the curve and the x-axis within that interval.