Question

Integral Equals Area under Curve Sine(x)

In calculus, what principle states that the integral of the sine function over a certain interval is equal to the area under the sine curve?

A) Fundamental Theorem of Calculus
B) Area Under Curve Theorem
C) Sine Integral Rule
D) Trigonometric Integration Law

Answer 1

The principle that states that the integral of the sine function over a certain interval is equal to the area under the sine curve is called the Fundamental Theorem of Calculus.

Step-by-step explanation:

The principle that states that the integral of the sine function over a certain interval is equal to the area under the sine curve is called the Fundamental Theorem of Calculus. This theorem establishes a fundamental connection between the concepts of differentiation and integration in calculus.

One way to understand this principle is to consider the area under the curve of the sine function between two points on the x-axis. By integrating the sine function over this interval, we can calculate the exact area enclosed by the curve and the x-axis.

For example, if we want to find the area under the sine curve between x = 0 and x = π, we can evaluate the integral of sine(x) from 0 to π. The result of this integral will be the exact area under the curve between these two points on the x-axis.